Notes on the Stationary p-Laplace Equation [electronic resource] / by Peter Lindqvist
- Lindqvist, Peter
- Cham : Springer International Publishing : Imprint: Springer, 2019.
- Physical Description:
- XI, 104 pages 2 illustrations, 1 illustration in color : online resource
- Additional Creators:
- SpringerLink (Online service)
- SpringerBriefs in Mathematics, 2191-8198
- 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.
- 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.
- Digital File Characteristics:
- text file PDF
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