· 2018
Nonlinear Potential Theory of Degenerate Elliptic Equations
- 1,799citations
- 2018year
Short summary
This text provides a self-contained treatment of the nonlinear potential theory of superharmonic functions, suitable for advanced students.
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Key points
- Develops nonlinear potential theory for superharmonic functions.
- Covers weighted Sobolev spaces and variational capacity.
- Investigates solutions to degenerate elliptic equations.
- Defines superharmonic functions via the comparison principle.
AI-generated from the title and abstract; the full text is not read.
Abstract
A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions.Starting with the theory of weighted Sobolev spaces, this treatment advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and ch
The authors' abstract, as published at the source., 2018 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics