Notes on the Stationary P-Laplace Equation

ISBN-13: 9783030145002 / Angielski / Miękka / 2019 / 104 str.

Peter Lindqvist

Recenzje

"The book will provide the reader with an up-to-date overview on the p-Laplace equation and will uncover ideas behind some concepts and involved results in the field." (Vladimir Bobkov, Mathematical Reviews, December, 2019)
"The book is a very useful contribution to the growing literature on this circle of ideas. I wholeheartedly recommend this book both as a textbook, as well as for independent study." (Vicentiu D. Radulescu, zbMATH 1421.35002, 2019)

Spis treści

1 Introduction.- 2 The Dirichlet problem and weak solutions.- 3 Regularity theory.- 4 Differentiability.- 5 On p-superharmonic functions.- 6 Perron's method.- 7 Some remarks in the complex plane.- 8 The infinity Laplacian.- 9 Viscosity solutions.- 10 Asymptotic mean values.- 11 Some open problems.- 12 Inequalities for vectors.

O autorze

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”.

Blurb

This book in the BCAM SpringerBriefs series is a treatise on the p-Laplace equation. It is based on lectures by the author that were originally delivered at the Summer School in Jyväskylä, Finland, in August 2005 and have since been updated and extended to cover various new topics, including viscosity solutions and asymptotic mean values. The p-Laplace equation is a far-reaching generalization of the ordinary Laplace equation, but it is non-linear and degenerate (p>2) or singular (p<2). Thus it requires advanced methods. Many fascinating properties of the Laplace equation are, in some modified version, extended to the p-Laplace equation. Nowadays the theory is almost complete, although some challenging problems remain open.