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.

Autorentext
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"

Klappentext
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.

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.