Notes on the Infinity-Laplace Equation

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.

List 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.

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"

Summary

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.

Report

"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)

Product details

• Authors: Peter Lindqvist
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 26.04.2016
• EAN: 9783319315317
• ISBN: 978-3-31-931531-7
• No. of pages: 68
• Dimensions: 155 mm x 234 mm x 6 mm
• Weight: 147 g
• Illustrations: IX, 68 p. 1 illus. in color.
• Series: SpringerBriefs in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Analysis, C, Computer Vision, Image Processing and Computer Vision, Mathematics and Statistics, Ordinary Differential Equations, Computer mathematics, Partial Differential Equations, Differential calculus & equations, Differential equations, Computational Science and Engineering, Maths for scientists, Optical data processing, Image processing