Notes on the Stationary p-Laplace Equation

1. Auflage 2019
ISBN: 978-3-030-14500-2
Verlag: Springer International Publishing

Buch, Englisch, 104 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 189 g

Reihe: SpringerBriefs in Mathematics

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.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Lindqvist, Peter

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.

Über Autor(innen)

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”.