Overview
- Authors:
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David Gilbarg
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Department of Mathematics, Stanford University, Stanford, USA
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Neil S. Trudinger
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Department of Pure Mathematics, Australian National University, Canberra, Australia
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Table of contents (15 chapters)
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Introduction
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- David Gilbarg, Neil S. Trudinger
Pages 1-9
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Linear Equations
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- David Gilbarg, Neil S. Trudinger
Pages 13-29
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- David Gilbarg, Neil S. Trudinger
Pages 30-49
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- David Gilbarg, Neil S. Trudinger
Pages 50-67
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- David Gilbarg, Neil S. Trudinger
Pages 68-81
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- David Gilbarg, Neil S. Trudinger
Pages 82-136
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- David Gilbarg, Neil S. Trudinger
Pages 137-165
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- David Gilbarg, Neil S. Trudinger
Pages 166-200
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Quasilinear Equations
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Front Matter
Pages 201-201
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- David Gilbarg, Neil S. Trudinger
Pages 203-220
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- David Gilbarg, Neil S. Trudinger
Pages 221-238
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- David Gilbarg, Neil S. Trudinger
Pages 239-263
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- David Gilbarg, Neil S. Trudinger
Pages 264-277
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- David Gilbarg, Neil S. Trudinger
Pages 278-299
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- David Gilbarg, Neil S. Trudinger
Pages 300-327
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- David Gilbarg, Neil S. Trudinger
Pages 328-380
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Back Matter
Pages 381-404
About this book
This volume is intended as an essentially self contained exposition of portions of the theory of second order quasilinear elliptic partial differential equations, with emphasis on the Dirichlet problem in bounded domains. It grew out of lecture notes for graduate courses by the authors at Stanford University, the final material extending well beyond the scope of these courses. By including preparatory chapters on topics such as potential theory and functional analysis, we have attempted to make the work accessible to a broad spectrum of readers. Above all, we hope the readers of this book will gain an appreciation of the multitude of ingenious barehanded techniques that have been developed in the study of elliptic equations and have become part of the repertoire of analysis. Many individuals have assisted us during the evolution of this work over the past several years. In particular, we are grateful for the valuable discussions with L. M. Simon and his contributions in Sections 15.4 to 15.8; for the helpful comments and corrections of J. M. Cross, A. S. Geue, J. Nash, P. Trudinger and B. Turkington; for the contributions of G. Williams in Section 10.5 and of A. S. Geue in Section 10.6; and for the impeccably typed manuscript which resulted from the dedicated efforts oflsolde Field at Stanford and Anna Zalucki at Canberra. The research of the authors connected with this volume was supported in part by the National Science Foundation.
Authors and Affiliations
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Department of Mathematics, Stanford University, Stanford, USA
David Gilbarg
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Department of Pure Mathematics, Australian National University, Canberra, Australia
Neil S. Trudinger
