Nonlinear Potential Theory of Degenerate Elliptic Equations

Heinonen, Juha/ Kipelainen, Tero/ Martio, Olli

ISBN 10: 048682425X / ISBN 13: 9780486824253

Published by Dover Pubns, 2018

About this Item

reprint edition. 416 pages. 8.25x5.50x1.00 inches. In Stock.

Seller Inventory # 048682425X

Bibliographic Details

• Title: Nonlinear Potential Theory of Degenerate Elliptic Equations
• Publisher: Dover Pubns
• Publication Date: 2018
• Language: English
• ISBN 10: 048682425X
• ISBN 13: 9780486824253
• Binding: Paperback
• Condition: Brand New
• Weight: 0.48 kilograms

About this title

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.

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.