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  • Book
  • © 2016

Notes on the Infinity Laplace Equation

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
    PDF

  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
    PDF
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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.
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Keywords

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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)
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Authors and Affiliations

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

    Peter Lindqvist

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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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Bibliographic Information

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Buy it now

eBook USD 19.99 USD 39.99
50% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 29.99 USD 54.99
45% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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