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Notes on the Infinity Laplace Equation

  • Book
  • © 2016

Overview

Authors:
  1. Peter Lindqvist

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

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  • Provides concise though comprehensive overview on the topic
  • This book will appeal to a wide readership, from graduate students to researchers
  • Enriches understanding on the topic
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Peter Lindqvist
    Pages 1-6

  3. Preliminaries

    • Peter Lindqvist
    Pages 7-14

  4. Variational Solutions

    • Peter Lindqvist
    Pages 15-22

  5. Viscosity Solutions

    • Peter Lindqvist
    Pages 23-31

  6. An Asymptotic Mean Value Formula

    • Peter Lindqvist
    Pages 33-37

  7. Comparison with Cones

    • Peter Lindqvist
    Pages 39-44

  8. From the Theory of Viscosity Solutions

    • Peter Lindqvist
    Pages 45-47

  9. Uniqueness of Viscosity Solutions

    • Peter Lindqvist
    Pages 49-54

  10. Tug-of-War

    • Peter Lindqvist
    Pages 55-56

  11. The Equation \(\Delta _{\infty }v = F\)

    • Peter Lindqvist
    Pages 57-66

  12. Back Matter

    Pages 67-68
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Keywords

About this book

This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author.  The Infinity-Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.

Reviews

“This book is an excellent introduction to the infinity Laplacian— it is informative and has up-to-date references.” (Fernando Charro, Mathematical Reviews, April 2017)

Authors and Affiliations

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

    Peter Lindqvist

About the author

Peter Lindqvist
Professor of Mathematics
Department of Mathematical Sciences
Norwegian University of Science and Technology
Trondheim, Norway

Research interests: Analysis, in particular partial differential equations and "nonlinear potential theory"

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