Notes on the Infinity Laplace Equation

by Peter Lindqvist

Overview

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.

Product Details

ISBN-13:	9783319315324
Publisher:	Springer-Verlag New York, LLC
Publication date:	05/25/2016
Series:	SpringerBriefs in Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	68
File size:	2 MB

About the Author

Peter LindqvistProfessor 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"

Table of Contents

1 Introduction.- 2 Preliminaries.- 3 Variational Solutions.- 4 Viscosity Solutions.- 5 An Asymptotic Mean Value Formula.- 6 Comparison with Cones.- 7 From the Theory of Viscosity Solutions.- 8 Uniqueness of Viscosity Solutions.- 9 Tug-of-War.- 10 The Equation 1v = F.

Editorial 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)

From the Publisher