Partial Differential Equations : : A unified Hilbert Space Approach / / Rainer Picard, Des McGhee.
This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space s...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2011] ©2011 |
Year of Publication: | 2011 |
Language: | English |
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Picard, Rainer, author. aut http://id.loc.gov/vocabulary/relators/aut Partial Differential Equations : A unified Hilbert Space Approach / Rainer Picard, Des McGhee. Berlin ; Boston : De Gruyter, [2011] ©2011 1 online resource (469 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Expositions in Mathematics , 0938-6572 ; 55 Frontmatter -- Preface -- Contents -- Nomenclature -- Chapter 1 Elements of Hilbert Space Theory -- Chapter 2 Sobolev Lattices -- Chapter 3 Linear Partial Differential Equations with Constant Coefficients in Rn+1, n ∈ N -- Chapter 4 Linear Evolution Equations -- Chapter 5 Some Evolution Equations of Mathematical Physics -- Chapter 6 A “Royal Road” to Initial Boundary Value Problems of Mathematical Physics -- Conclusion -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space setting (rather than on an apparently more general Banach space) is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations, which consider either specific equation types or apply a collection of tools for solving a variety of equations, this book takes a more global point of view by focusing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can be naturally developed. Applications to many areas of mathematical physics are also presented. The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and also for researchers, who will find new results for particular evolutionary systems from mathematical physics. 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 28. Feb 2023) Differential equations, Partial. Hilbert space. Evolution Equation. Hilbert Space. Mathematics. Partial Differential Equations. Sobolev. MATHEMATICS / Differential Equations / General. bisacsh McGhee, Des, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package 9783110494969 ZDB-23-EXM Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2010 9783110233544 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2010 9783110233551 Title is part of eBook package: De Gruyter E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2010 9783110233636 ZDB-23-DMN print 9783110250268 https://doi.org/10.1515/9783110250275 https://www.degruyter.com/isbn/9783110250275 Cover https://www.degruyter.com/document/cover/isbn/9783110250275/original |
language |
English |
format |
eBook |
author |
Picard, Rainer, Picard, Rainer, McGhee, Des, |
spellingShingle |
Picard, Rainer, Picard, Rainer, McGhee, Des, Partial Differential Equations : A unified Hilbert Space Approach / De Gruyter Expositions in Mathematics , Frontmatter -- Preface -- Contents -- Nomenclature -- Chapter 1 Elements of Hilbert Space Theory -- Chapter 2 Sobolev Lattices -- Chapter 3 Linear Partial Differential Equations with Constant Coefficients in Rn+1, n ∈ N -- Chapter 4 Linear Evolution Equations -- Chapter 5 Some Evolution Equations of Mathematical Physics -- Chapter 6 A “Royal Road” to Initial Boundary Value Problems of Mathematical Physics -- Conclusion -- Bibliography -- Index |
author_facet |
Picard, Rainer, Picard, Rainer, McGhee, Des, McGhee, Des, McGhee, Des, |
author_variant |
r p rp r p rp d m dm |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
McGhee, Des, McGhee, Des, |
author2_variant |
d m dm |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Picard, Rainer, |
title |
Partial Differential Equations : A unified Hilbert Space Approach / |
title_sub |
A unified Hilbert Space Approach / |
title_full |
Partial Differential Equations : A unified Hilbert Space Approach / Rainer Picard, Des McGhee. |
title_fullStr |
Partial Differential Equations : A unified Hilbert Space Approach / Rainer Picard, Des McGhee. |
title_full_unstemmed |
Partial Differential Equations : A unified Hilbert Space Approach / Rainer Picard, Des McGhee. |
title_auth |
Partial Differential Equations : A unified Hilbert Space Approach / |
title_alt |
Frontmatter -- Preface -- Contents -- Nomenclature -- Chapter 1 Elements of Hilbert Space Theory -- Chapter 2 Sobolev Lattices -- Chapter 3 Linear Partial Differential Equations with Constant Coefficients in Rn+1, n ∈ N -- Chapter 4 Linear Evolution Equations -- Chapter 5 Some Evolution Equations of Mathematical Physics -- Chapter 6 A “Royal Road” to Initial Boundary Value Problems of Mathematical Physics -- Conclusion -- Bibliography -- Index |
title_new |
Partial Differential Equations : |
title_sort |
partial differential equations : a unified hilbert space approach / |
series |
De Gruyter Expositions in Mathematics , |
series2 |
De Gruyter Expositions in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2011 |
physical |
1 online resource (469 p.) Issued also in print. |
contents |
Frontmatter -- Preface -- Contents -- Nomenclature -- Chapter 1 Elements of Hilbert Space Theory -- Chapter 2 Sobolev Lattices -- Chapter 3 Linear Partial Differential Equations with Constant Coefficients in Rn+1, n ∈ N -- Chapter 4 Linear Evolution Equations -- Chapter 5 Some Evolution Equations of Mathematical Physics -- Chapter 6 A “Royal Road” to Initial Boundary Value Problems of Mathematical Physics -- Conclusion -- Bibliography -- Index |
isbn |
9783110250275 9783110494969 9783110238570 9783110238471 9783110637205 9783110233544 9783110233551 9783110233636 9783110250268 |
issn |
0938-6572 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA322 |
callnumber-sort |
QA 3322.4 P53 42011 |
url |
https://doi.org/10.1515/9783110250275 https://www.degruyter.com/isbn/9783110250275 https://www.degruyter.com/document/cover/isbn/9783110250275/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515/.733 |
dewey-sort |
3515 3733 |
dewey-raw |
515/.733 |
dewey-search |
515/.733 |
doi_str_mv |
10.1515/9783110250275 |
oclc_num |
753970239 |
work_keys_str_mv |
AT picardrainer partialdifferentialequationsaunifiedhilbertspaceapproach AT mcgheedes partialdifferentialequationsaunifiedhilbertspaceapproach |
status_str |
n |
ids_txt_mv |
(DE-B1597)122836 (OCoLC)753970239 |
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is_hierarchy_title |
Partial Differential Equations : A unified Hilbert Space Approach / |
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