Nonlinear Potential Theory of Degenerate Elliptic Equations
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Nonlinear Potential Theory of Degenerate Elliptic Equations by John Dirk Walecka
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.
Heinonen, Juha: - Juha Heinonen (1960-2007) was Professor of Mathematics at the University of Michigan. His principal areas of research interest included quasiconformal mappings, nonlinear potential theory, and analysis on metric spaces. He was the author of over 60 research articles, including several posthumously, and two textbooks. A member of the Finnish Academy of Science and Letters, Heinonen received the Excellence in Research Award from the University of Michigan in 1997 and gave an invited lecture at the International Congress of Mathematicians in Beijing in 2002.
| SKU | Unavailable |
| ISBN 13 | 9780486824253 |
| ISBN 10 | 048682425X |
| Title | Nonlinear Potential Theory of Degenerate Elliptic Equations |
| Author | John Dirk Walecka |
| Condition | Unavailable |
| Binding type | Paperback |
| Publisher | Dover Publications Inc. |
| Year published | 2018-06-29 |
| Number of pages | 416 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |