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.
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.
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)
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
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&ll£‡
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