| Description |
1 online resource (416 pages) |
| Access |
Access limited to subscribing institutions. |
| Summary |
A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume 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, the text 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 chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes. |
| Note |
Print version record. |
| Subject |
Calculus of variations.
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Differential equations, Elliptic.
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Potential theory (Mathematics)
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MATHEMATICS / Functional Analysis.
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| Genre/Form |
Electronic books.
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| Added Author |
Kilpeläinen, Tero, author.
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Martio, O. (Olli), author.
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| Other Form: |
Print version: Heinonen, Juha. Nonlinear potential theory of degenerate elliptic equations. Mineola, New York : Dover Publications, Inc., 2018. 9780486824253 (pbk.) (DLC)2017053600 |
| Standard No. |
9780486830469 |
| ISBN |
9780486830469 (epub) |
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