- Treatise on the p-Laplace equation
- Coverage of a variety of topics
- Discussion of open problems
Buy this book
- About this book
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This book in the BCAM SpringerBriefs series is a treatise on the p-Laplace equation. It is based on lectures by the author that were originally delivered at the Summer School in Jyväskylä, Finland, in August 2005 and have since been updated and extended to cover various new topics, including viscosity solutions and asymptotic mean values. The p-Laplace equation is a far-reaching generalization of the ordinary Laplace equation, but it is non-linear and degenerate (p>2) or singular (p<2). Thus it requires advanced methods. Many fascinating properties of the Laplace equation are, in some modified version, extended to the p-Laplace equation. Nowadays the theory is almost complete, although some challenging problems remain open.
- About the authors
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Peter Lindqvist is Professor of Mathematics in the Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway. His research focus is analysis, including in particular partial differential equations and “non-linear potential theory”.
- Reviews
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“The book will provide the reader with an up-to-date overview on the p-Laplace equation and will uncover ideas behind some concepts and involved results in the field.” (Vladimir Bobkov, Mathematical Reviews, December, 2019)
“The book is a very useful contribution to the growing literature on this circle of ideas. I wholeheartedly recommend this book both as a textbook, as well as for independent study.” (Vicenţiu D. Rădulescu, zbMATH 1421.35002, 2019)
- Table of contents (12 chapters)
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Introduction
Pages 1-5
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The Dirichlet Problem and Weak Solutions
Pages 7-16
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Regularity Theory
Pages 17-28
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Differentiability
Pages 29-36
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On p-Superharmonic Functions
Pages 37-54
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Table of contents (12 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Notes on the Stationary p-Laplace Equation
- Authors
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- Peter Lindqvist
- Series Title
- SpringerBriefs in Mathematics
- Copyright
- 2019
- Publisher
- Springer International Publishing
- Copyright Holder
- The Author(s), under exclusive license to Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-14501-9
- DOI
- 10.1007/978-3-030-14501-9
- Softcover ISBN
- 978-3-030-14500-2
- Series ISSN
- 2191-8198
- Edition Number
- 1
- Number of Pages
- XI, 104
- Number of Illustrations
- 1 b/w illustrations, 1 illustrations in colour
- Topics
