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Nonlinear Potential Theory of Degenerate Elliptic Equations (Dover Books on Mathematics) - Softcover
Synopsis
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.
"synopsis" may belong to another edition of this title.
About the Author
Juha Heinonen, Assistant Professor of Mathematics, University of Michigan. Tero Kilpelainen, Docent of Mathematics, University of Jyvaskyla. Olli Martio, Professor, Department of Mathematics, University of Jyvaskyla.
Review
'excellent book'
S.K. Vodopyanov, Mathematical Reviews, Issue 94e
`The book is warmly recommended to specialists in potential theory, elliptic PDE's, Sobolev spaces and quasiconformal mappings.'
European Mathematical Society Newsletter, No. 11, 1994
`In particular, the theory of the (degenerate) eliptic equations . . . is very readable and very comprehensively presented. . . . This is a highly recommendable, solid introduction to the nonlinear potential theory, compulsory reading for everyone who would like to work in this field.'
Deutschen Mathematiker-Vereinigung
"About this title" may belong to another edition of this title.
- PublisherDover
- Publication date2018
- ISBN 10 048682425X
- ISBN 13 9780486824253
- BindingPaperback
- LanguageEnglish
- Number of pages416
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Paperback. Condition: new. Paperback. 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 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 text concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes. 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. 1993 edition. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780486824253
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