Nonlinear second order elliptic equations involving measures / Moshe Marcus, Laurent Véron.

Format:

Book

Author/Creator:

Marcus, M. (Moshe), 1937-

Contributor:

Véron, Laurent.

Series:

De Gruyter Series in Nonlinear Analysis and Applications

De Gruyter series in nonlinear analysis and applications, 0941-813X ; 21

De Gruyter Series in Nonlinear Analysis and Applications ; 21

Language:

English

Subjects (All):

Differential equations, Elliptic.

Differential equations, Nonlinear.

Physical Description:

1 online resource (264 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : Walter de Gruyter GmbH & Co. KG, [2014]

Language Note:

English

Summary:

In the last 40 years semi-linear elliptic equations became a central subject of study in the theory of nonlinear partial differential equations. On the one hand, the interest in this area is of a theoretical nature, due to its deep relations to other branches of mathematics, especially linear and nonlinear harmonic analysis, dynamical systems, differential geometry and probability. On the other hand, this study is of interest because of its applications. Equations of this type come up in various areas such as problems of physics and astrophysics, curvature problems in Riemannian geometry, logistic problems related for instance to population models and, most importantly, the study of branching processes and superdiffusions in the theory of probability. The aim of this book is to present a comprehensive study of boundary value problems for linear and semi-linear second order elliptic equations with measure data. We are particularly interested in semi-linear equations with absorption. The interactions between the diffusion operator and the absorption term give rise to a large class of nonlinear phenomena in the study of which singularities and boundary trace play a central role. This book is accessible to graduate students and researchers with a background in real analysis and partial differential equations.

Contents:

Frontmatter

Preface

Contents

Chapter 1. Linear second order elliptic equations with measure data

Chapter 2. Nonlinear second order elliptic equations with measure data

Chapter 3. The boundary trace and associated boundary value problems

Chapter 4. Isolated singularities

Chapter 5. Classical theory of maximal and large solutions

Chapter 6. Further results on singularities and large solutions

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9783110305319

3110305313

OCLC:

865329714