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by Juha Heinonen,Tero Kilpeläinen,Olli Martio
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ISBN: 0486450503 Dover Publications Price: $19.95 |
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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.
Slightly corrected republication of the edition published by Oxford University Press, New York, 1993.
Table of Contents for Nonlinear Potential Theory of Degenerate Elliptic Equations
| Introduction | |||||||
| 1. Weighted Sobolev spaces | |||||||
| 2. Capacity | |||||||
| 3. Supersolutions and the obstacle problem | |||||||
| 4. Refined Sobolev spaces | |||||||
| 5. Variational integrals | |||||||
| 6. Harmonic functions | |||||||
| 7. Superharmonic functions | |||||||
| 8. Balayage | |||||||
| 9. Perron's method, barriers, and resolutivity | |||||||
| 10. Polar sets | |||||||
| 11. Harmonic measure | |||||||
| 12. Fine topology | |||||||
| 13. Harmonic morphisms | |||||||
| 14. Quasiregular mappings | |||||||
| 15. Ap-weights and Jacobians of quasiconformal mappings | |||||||
| 16. Axiomatic nonlinear potential theory | |||||||
| 17. Appendix I: The existence of solutions | |||||||
| 18. Appendix II: The John-Nirenberg lemma | |||||||
| Bibliography | |||||||
| List of symbols | |||||||
| Index |