Nonlinear Potential Theory of Degenerate Elliptic Equations by John Dirk Walecka

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Nonlinear Potential Theory of Degenerate Elliptic Equations by John Dirk Walecka

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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.

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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 Non disponible
ISBN 13 9780486824253
ISBN 10 048682425X
Titre Nonlinear Potential Theory of Degenerate Elliptic Equations
Auteur John Dirk Walecka
État Non disponible
Type de reliure Paperback
Éditeur Dover Publications Inc.
Année de publication 2018-06-29
Nombre de pages 416
Note de couverture La photo du livre est présentée à titre d'illustration uniquement. La reliure, la couverture ou l'édition réelle peuvent varier.
Note Non disponible