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.

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

Autorentext

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".

Inhalt
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.