Singular Solutions of Nonlinear Elliptic and Parabolic Equations / / Alexander A. Kovalevsky, Igor I. Skrypnik, Andrey E. Shishkov.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2016 Part 1
• VerfasserIn: Kovalevsky, Alexander A.,; Shishkov, Andrey E.,; Skrypnik, Igor I.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2016]; ©2016
• Year of Publication: 2016
• Language: English
• Series: De Gruyter Series in Nonlinear Analysis and Applications , 24
• Physical Description: 1 online resource (XII, 435 p.)

This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form.The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis.Contents:ForewordPart I: Nonlinear elliptic equations with L^1-dataNonlinear elliptic equations of the second order with L^1-dataNonlinear equations of the fourth order with strengthened coercivity and L^1-dataPart II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second orderRemovability of singularities of the solutions of quasilinear elliptic equationsRemovability of singularities of the solutions of quasilinear parabolic equationsQuasilinear elliptic equations with coefficients from the Kato classPart III: Boundary regimes with peaking for quasilinear parabolic equationsEnergy methods for the investigation of localized regimes with peaking for parabolic second-order equationsMethod of functional inequalities in peaking regimes for parabolic equations of higher ordersNonlocalized regimes with singular peakingAppendix: Formulations and proofs of the auxiliary resultsBibliography

Table of Contents

Frontmatter -- Foreword -- Contents -- Part I. Nonlinear elliptic equations with L1-data -- Chapter 1. Nonlinear elliptic equations of the second order with L1-data -- Chapter 2. Nonlinear equations of the fourth order with strengthened coercivity and L1-data -- Part II. Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order -- Chapter 3. Removability of singularities of the solutions of quasilinear elliptic equations -- Chapter 4. Removability of singularities of the solutions of quasilinear parabolic equations -- Chapter 5. Quasilinear elliptic equations with coefficients from the Kato class -- Part III. Boundary regimes with peaking for quasilinear parabolic equations -- Chapter 6. Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations -- Chapter 7. Method of functional inequalities in peaking regimes for parabolic equations of higher orders -- Chapter 8. Nonlocalized regimes with singular peaking -- Chapter 9. Appendix: Formulations and proofs of the auxiliary results -- Bibliography -- Backmatter