Lindqvist Notes on the Infinity Laplace Equation

1. Auflage 2016
ISBN: 978-3-319-31532-4
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 68 Seiten, eBook

Reihe: SpringerBriefs in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Lindqvist, Peter

Inhaltsverzeichnis

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.

Über Autor(innen)

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"