Nonlinear Potential Theory Of Degenerate Elliptic Equations

by Juha Heinonen, Tero Kilpeläinen And Olli Martio

• ISBN13: 9780486450506
• ISBN10: 0486450503
• Format: Paperback
• Copyright: 2006-10-06
• Publisher: Dover Publications

Summary

This text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Topics include the theory of weighted variational capacity; solutions and supersolutions of equation; balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; more. 1993 edition.

Table of Contents

Preface to the Dover Edition	vii
Corrigenda	ix
Introduction	1	(192)
1. Weighted Sobolev spaces	7	(20)
2. Capacity	27	(28)
3. Supersolutions and the obstacle problem	55	(32)
4. Refined Sobolev spaces	87	(10)
5. Variational integrals	97	(13)
6. A-harmonic functions	110	(21)
7. A-superharmonic functions	131	(26)
8. Balayage	157	(11)
9. Perron's method, barriers, and resolutivity	168	(25)
10. Polar sets	193	(8)
11. A-harmonic measure	201	(16)
12. Fine topology	217	(19)
13. Harmonic morphisms	236	(14)
14. Quasiregular mappings	250	(47)
15. Ap-weights and Jacobians of quasiconformal mappings	297	(20)
16. Axiomatic nonlinear potential theory	317	(15)
17. Appendix I: The existence of solutions	332	(4)
18. Appendix II: The John—Nirenberg lemma	336	(6)
Bibliography	342	(14)
List of symbols	356	(4)
Index	360	(5)
Epilogue
19. The John-Nirenberg lemma	365	(7)
20. Admissible Weights	372	(9)
21. The Riesz measure of an A-superharmonic function	381	(13)
22. Generalizations	394	(4)
New Bibliography	398