دانلود کتاب Nonlinear Potential Theory of Degenerate Elliptic Equations

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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. Perron’s 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