Singular solutions of nonlinear elliptic and parabolic equations / Alexander A. Kovalevsky, Igor I. Skrypnik, Andrey E. Shishkov.

Format:

Book

Author/Creator:

Kovalevsky, Alexander A., author.

Skrypnik, Igor I., author.

Shishkov, Andrey E., author.

Series:

De Gruyter series in nonlinear analysis and applications ; Volume 24.

De Gruyter Series in Nonlinear Analysis and Applications, 0941-813X ; Volume 24

Language:

English

Subjects (All):

Differential equations, Elliptic.

Differential equations, Nonlinear.

Differential equations, Parabolic.

Physical Description:

1 online resource (448 p.)

Edition:

1st ed.

Place of Publication:

Berlin, [Germany] ; Boston, [Massachusetts] : de Gruyter, 2016.

Language Note:

English

Summary:

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: Foreword Part 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 order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography

Contents:

Front matter

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

Back matter

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

9783110332247

3110332248

9783110390087

3110390086

OCLC:

939911315