Notes on the stationary p-Laplace equation

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 viscosi...

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Bibliographic Details
Main Author: Lindqvist, Peter (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham : Springer, 2019.
Series:SpringerBriefs in mathematics.
Physical Description:
1 online resource.
Subjects:
Differential equations, Elliptic.
Harmonic functions.
Online Access:SpringerLink - Click here for access

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505 0 |a Intro; Preface; About This Book; Contents; About the Author; 1 Introduction; 2 The Dirichlet Problem and Weak Solutions; 3 Regularity Theory; 3.1 The Case p>n; 3.2 The Case p=n; 3.3 The Case 1<p<n; 4 Differentiability; 5 On p-Superharmonic Functions; 5.1 Definition and Examples; 5.2 The Obstacle Problem and Approximation; 5.3 Infimal Convolutions; 5.4 The Poisson Modification; 5.5 Summability of Unbounded p-Superharmonic Functions; 5.6 About Pointwise Behaviour; 5.7 Summability of the Gradient; 6 Perron's Method; 7 Some Remarks in the Complex Plane; 8 The Infinity Laplacian. 
505 8 |a 9 Viscosity Solutions10 Asymptotic Mean Values; 11 Some Open Problems; 12 Inequalities for Vectors; Literature; References. 
520 |a 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. 
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