Nonlinear Potential Theory of Degenerate
β Juha Heinonen, Tero Kilpelainen, Olli Martio
π Library
π
2006
π Dover Publications
π English
β¦ LIBER β¦
π
Nonlinear Potential Theory of Degenerate Elliptic Equations
β Scribed by Juha Heinonen, Tero KilpelΓ€inen, Olli Martio
- Publisher
- Dover Publications
- Year
- 2006
- Tongue
- English
- Leaves
- 412
- Series
- Dover Books on Mathematics
- Edition
- Reprint
- Category
- Library
β¬ Acquire This Volume
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β¦ Synopsis
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.
β¦ Table of Contents
Preface to the Dover Edition vii
Corrigenda ix
Introduction 1
1. Weighted Sobolev spaces 7
2. Capacity 27
3. Supersolutions and the obstacle problem 55
4. Refined Sobolev spaces 87
5. Variational integrals 97
6. A-harmonic functions 110
7. A-superharmonic functions 131
8. Balayage 157
9. Perronβs method, barriers, and resolutivity 168
10. Polar sets 193
11. A-harmonic measure 201
12. Fine topology 217
13. Harmonic morphisms 236
14. Quasiregular mappings 250
15. Ap-weights and Jacobians of quasiconformal mappings 297
16. Axiomatic nonlinear potential theory 317
17. Appendix I: The existence of solutions 332
18. Appendix II: The John-Nirenberg lemma 336
Bibliography 342
List of symbols 356
Index 360
Epilogue
19. The John-Nirenberg lemma 365
20. Admissible Weights 372
21. The Riesz measure of an A-superharmonic function 381
22. Generalizations 394
New Bibliography 398
β¦ Subjects
Differential Equations;Applied;Mathematics;Science & Math;Game Theory;Applied;Mathematics;Science & Math;Calculus;Pure Mathematics;Mathematics;Science & Math;Calculus;Mathematics;Science & Mathematics;New, Used & Rental Textbooks;Specialty Boutique
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