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Notes on the Stationary p-Laplace Equation

  • Book
  • © 2019

Overview

Authors:
  1. Peter Lindqvist

    1. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

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  • Treatise on the p-Laplace equation
  • Coverage of a variety of topics
  • Discussion of open problems

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Peter Lindqvist
    Pages 1-5

  3. The Dirichlet Problem and Weak Solutions

    • Peter Lindqvist
    Pages 7-16

  4. Regularity Theory

    • Peter Lindqvist
    Pages 17-28

  5. Differentiability

    • Peter Lindqvist
    Pages 29-36

  6. On p-Superharmonic Functions

    • Peter Lindqvist
    Pages 37-54

  7. Perron’s Method

    • Peter Lindqvist
    Pages 55-63

  8. Some Remarks in the Complex Plane

    • Peter Lindqvist
    Pages 65-67

  9. The Infinity Laplacian

    • Peter Lindqvist
    Pages 69-75

  10. Viscosity Solutions

    • Peter Lindqvist
    Pages 77-85

  11. Asymptotic Mean Values

    • Peter Lindqvist
    Pages 87-93

  12. Some Open Problems

    • Peter Lindqvist
    Pages 95-96

  13. Inequalities for Vectors

    • Peter Lindqvist
    Pages 97-100

  14. Back Matter

    Pages 101-104
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Keywords

About this book

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.


Reviews

“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)


Authors and Affiliations

  • Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Peter Lindqvist

About the author

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”.

Bibliographic Information

  • Book Title: Notes on the Stationary p-Laplace Equation

  • Authors: Peter Lindqvist

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-14501-9

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

  • Softcover ISBN: 978-3-030-14500-2Published: 08 May 2019

  • eBook ISBN: 978-3-030-14501-9Published: 26 April 2019

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: XI, 104

  • Number of Illustrations: 1 b/w illustrations, 1 illustrations in colour

  • Topics: Mathematics, general

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