Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) / / Olivier Druet, Frédéric Robert, Emmanuel Hebey.
Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand sid...
Saved in:
Superior document: | Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 |
---|---|
VerfasserIn: | |
Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2009] ©2004 |
Year of Publication: | 2009 |
Edition: | Course Book |
Language: | English |
Series: | Mathematical Notes ;
45 |
Online Access: | |
Physical Description: | 1 online resource (224 p.) |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
9781400826162 |
---|---|
ctrlnum |
(DE-B1597)446346 (OCoLC)979578332 |
collection |
bib_alma |
record_format |
marc |
spelling |
Druet, Olivier, author. aut http://id.loc.gov/vocabulary/relators/aut Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) / Olivier Druet, Frédéric Robert, Emmanuel Hebey. Course Book Princeton, NJ : Princeton University Press, [2009] ©2004 1 online resource (224 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematical Notes ; 45 Frontmatter -- Contents -- Preface -- Chapter 1. Background Material -- Chapter 2. The Model Equations -- Chapter 3. Blow-up Theory in Sobolev Spaces -- Chapter 4. Exhaustion and Weak Pointwise Estimates -- Chapter 5. Asymptotics When the Energy Is of Minimal Type -- Chapter 6. Asymptotics When the Energy Is Arbitrary -- Appendix A. The Green's Function on Compact Manifolds -- Appendix B. Coercivity Is a Necessary Condition -- Bibliography restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand side and a critical nonlinearity on the right hand side. A significant development in the study of such equations occurred in the 1980s. It was discovered that the sequence splits into a solution of the limit equation--a finite sum of bubbles--and a rest that converges strongly to zero in the Sobolev space consisting of square integrable functions whose gradient is also square integrable. This splitting is known as the integral theory for blow-up. In this book, the authors develop the pointwise theory for blow-up. They introduce new ideas and methods that lead to sharp pointwise estimates. These estimates have important applications when dealing with sharp constant problems (a case where the energy is minimal) and compactness results (a case where the energy is arbitrarily large). The authors carefully and thoroughly describe pointwise behavior when the energy is arbitrary. Intended to be as self-contained as possible, this accessible book will interest graduate students and researchers in a range of mathematical fields. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) MATHEMATICS / Mathematical Analysis. bisacsh Asymptotic analysis. Cayley-Hamilton theorem. Contradiction. Curvature. Diffeomorphism. Differentiable manifold. Equation. Estimation. Euclidean space. Laplace's equation. Maximum principle. Nonlinear system. Polynomial. Princeton University Press. Result. Ricci curvature. Riemannian geometry. Riemannian manifold. Simply connected space. Sphere theorem (3-manifolds). Stone's theorem. Submanifold. Subsequence. Theorem. Three-dimensional space (mathematics). Topology. Unit sphere. Hebey, Emmanuel, author. aut http://id.loc.gov/vocabulary/relators/aut Robert, Frédéric, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 9783110494921 ZDB-23-PMN Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691119533 https://doi.org/10.1515/9781400826162 https://www.degruyter.com/isbn/9781400826162 Cover https://www.degruyter.com/document/cover/isbn/9781400826162/original |
language |
English |
format |
eBook |
author |
Druet, Olivier, Druet, Olivier, Hebey, Emmanuel, Robert, Frédéric, |
spellingShingle |
Druet, Olivier, Druet, Olivier, Hebey, Emmanuel, Robert, Frédéric, Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) / Mathematical Notes ; Frontmatter -- Contents -- Preface -- Chapter 1. Background Material -- Chapter 2. The Model Equations -- Chapter 3. Blow-up Theory in Sobolev Spaces -- Chapter 4. Exhaustion and Weak Pointwise Estimates -- Chapter 5. Asymptotics When the Energy Is of Minimal Type -- Chapter 6. Asymptotics When the Energy Is Arbitrary -- Appendix A. The Green's Function on Compact Manifolds -- Appendix B. Coercivity Is a Necessary Condition -- Bibliography |
author_facet |
Druet, Olivier, Druet, Olivier, Hebey, Emmanuel, Robert, Frédéric, Hebey, Emmanuel, Hebey, Emmanuel, Robert, Frédéric, Robert, Frédéric, |
author_variant |
o d od o d od e h eh f r fr |
author_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Hebey, Emmanuel, Hebey, Emmanuel, Robert, Frédéric, Robert, Frédéric, |
author2_variant |
e h eh f r fr |
author2_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author_sort |
Druet, Olivier, |
title |
Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) / |
title_full |
Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) / Olivier Druet, Frédéric Robert, Emmanuel Hebey. |
title_fullStr |
Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) / Olivier Druet, Frédéric Robert, Emmanuel Hebey. |
title_full_unstemmed |
Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) / Olivier Druet, Frédéric Robert, Emmanuel Hebey. |
title_auth |
Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) / |
title_alt |
Frontmatter -- Contents -- Preface -- Chapter 1. Background Material -- Chapter 2. The Model Equations -- Chapter 3. Blow-up Theory in Sobolev Spaces -- Chapter 4. Exhaustion and Weak Pointwise Estimates -- Chapter 5. Asymptotics When the Energy Is of Minimal Type -- Chapter 6. Asymptotics When the Energy Is Arbitrary -- Appendix A. The Green's Function on Compact Manifolds -- Appendix B. Coercivity Is a Necessary Condition -- Bibliography |
title_new |
Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) / |
title_sort |
blow-up theory for elliptic pdes in riemannian geometry (mn-45) / |
series |
Mathematical Notes ; |
series2 |
Mathematical Notes ; |
publisher |
Princeton University Press, |
publishDate |
2009 |
physical |
1 online resource (224 p.) Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Preface -- Chapter 1. Background Material -- Chapter 2. The Model Equations -- Chapter 3. Blow-up Theory in Sobolev Spaces -- Chapter 4. Exhaustion and Weak Pointwise Estimates -- Chapter 5. Asymptotics When the Energy Is of Minimal Type -- Chapter 6. Asymptotics When the Energy Is Arbitrary -- Appendix A. The Green's Function on Compact Manifolds -- Appendix B. Coercivity Is a Necessary Condition -- Bibliography |
isbn |
9781400826162 9783110494921 9783110442502 9780691119533 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA315 |
callnumber-sort |
QA 3315 D78 42004 |
url |
https://doi.org/10.1515/9781400826162 https://www.degruyter.com/isbn/9781400826162 https://www.degruyter.com/document/cover/isbn/9781400826162/original |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9781400826162 |
oclc_num |
979578332 |
work_keys_str_mv |
AT druetolivier blowuptheoryforellipticpdesinriemanniangeometrymn45 AT hebeyemmanuel blowuptheoryforellipticpdesinriemanniangeometrymn45 AT robertfrederic blowuptheoryforellipticpdesinriemanniangeometrymn45 |
status_str |
n |
ids_txt_mv |
(DE-B1597)446346 (OCoLC)979578332 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
is_hierarchy_title |
Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) / |
container_title |
Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 |
author2_original_writing_str_mv |
noLinkedField noLinkedField noLinkedField noLinkedField |
_version_ |
1770176642049638400 |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05518nam a22010455i 4500</leader><controlfield tag="001">9781400826162</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20220131112047.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">220131t20092004nju fo d z eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400826162</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400826162</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)446346</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)979578332</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">nju</subfield><subfield code="c">US-NJ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA315.D78 2004</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT034000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Druet, Olivier, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45) /</subfield><subfield code="c">Olivier Druet, Frédéric Robert, Emmanuel Hebey.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Course Book</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ : </subfield><subfield code="b">Princeton University Press, </subfield><subfield code="c">[2009]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (224 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematical Notes ;</subfield><subfield code="v">45</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">Preface -- </subfield><subfield code="t">Chapter 1. Background Material -- </subfield><subfield code="t">Chapter 2. The Model Equations -- </subfield><subfield code="t">Chapter 3. Blow-up Theory in Sobolev Spaces -- </subfield><subfield code="t">Chapter 4. Exhaustion and Weak Pointwise Estimates -- </subfield><subfield code="t">Chapter 5. Asymptotics When the Energy Is of Minimal Type -- </subfield><subfield code="t">Chapter 6. Asymptotics When the Energy Is Arbitrary -- </subfield><subfield code="t">Appendix A. The Green's Function on Compact Manifolds -- </subfield><subfield code="t">Appendix B. Coercivity Is a Necessary Condition -- </subfield><subfield code="t">Bibliography</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand side and a critical nonlinearity on the right hand side. A significant development in the study of such equations occurred in the 1980s. It was discovered that the sequence splits into a solution of the limit equation--a finite sum of bubbles--and a rest that converges strongly to zero in the Sobolev space consisting of square integrable functions whose gradient is also square integrable. This splitting is known as the integral theory for blow-up. In this book, the authors develop the pointwise theory for blow-up. They introduce new ideas and methods that lead to sharp pointwise estimates. These estimates have important applications when dealing with sharp constant problems (a case where the energy is minimal) and compactness results (a case where the energy is arbitrarily large). The authors carefully and thoroughly describe pointwise behavior when the energy is arbitrary. Intended to be as self-contained as possible, this accessible book will interest graduate students and researchers in a range of mathematical fields.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Mathematical Analysis.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Asymptotic analysis.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Cayley-Hamilton theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Contradiction.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Curvature.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Diffeomorphism.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Differentiable manifold.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Estimation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Euclidean space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Laplace's equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Maximum principle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Nonlinear system.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Polynomial.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Princeton University Press.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Result.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Ricci curvature.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Riemannian geometry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Riemannian manifold.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Simply connected space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Sphere theorem (3-manifolds).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Stone's theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Submanifold.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Subsequence.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Three-dimensional space (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Topology.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Unit sphere.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Hebey, Emmanuel, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Robert, Frédéric, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton Mathematical Notes eBook-Package 1970-2016</subfield><subfield code="z">9783110494921</subfield><subfield code="o">ZDB-23-PMN</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton University Press eBook-Package Backlist 2000-2013</subfield><subfield code="z">9783110442502</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9780691119533</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400826162</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9781400826162</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/document/cover/isbn/9781400826162/original</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-044250-2 Princeton University Press eBook-Package Backlist 2000-2013</subfield><subfield code="c">2000</subfield><subfield code="d">2013</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_BACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_PPALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA12STME</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA13ENGE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA18STMEE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA5EBK</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-PMN</subfield><subfield code="c">1970</subfield><subfield code="d">2016</subfield></datafield></record></collection> |