Potential theory for Helmholtz operator and nonlinear eigenvalue problems

Chapters in this book

1. I-XII I
2. Invited Lectures
3. Lp potential theory techniques and nonlinear PDE 1
4. Applications of Choquet theory to potential theory 17
5. One version non linéaire du théorème de Hunt 25
6. Strict isoperimetric inequalities and asymmetry 33
7. Nonlinear potential theory 43
8. Potential theory and quasiconformal mappings 55
9. Maximal inequalities and potential theory 65
10. The boundary behaviour of solutions of the Dirichlet problem 75
11. Capacities in function theory 93
12. Potential theory on non-locally compact space via Dirichlet forms 107
13. The Martin compactification of a symmetric space of non-compact type at the bottom of the positive spectrum : An introduction 127
14. Level sets and the Green function 141
15. Contributed Papers
16. Local properties of solutions to equations involving square Hörmander’s operators 147
17. On the generalized Neumann problem 155
18. Principe de Picard pour les mesures invariantes par rotation et applications 161
19. Measure and capacity of exceptional sets arising in estimations of δ-subharmonic functions 171
20. Balayage spaces, standard Η-cones and hyperharmonic cones 179
21. On the thermoelastic potential in three-dimensional hyperbolic thermoelasticity theory 193
22. Representations and estimates for inverse operators of the potential theory integral equations in a polyhedron 201
23. Use of single layer potential in mixed problems of elasticity 207
24. Discretization of bounded harmonic functions on Riemannian manifolds and entropy 213
25. Capacities and mappings quasiconformal in the mean 225
26. Beppo Levi spaces and Riesz potential spaces 229
27. Boundary limits of harmonic functions in Sobolev-Orlicz classes 235
28. Positive harmonic functions on rotationary symmetric Riemannian manifolds 251
29. Examples of stable Martin boundaries of Markov chains 261
30. Comparison of liminf and fine liminf of positive superharmonic functions 271
31. Some problems of the potential theory for Schrödinger operator with singular potential 275
32. Potential theory for Helmholtz operator and nonlinear eigenvalue problems 281
33. On stationary points of the energy integral 291
34. Application of potential theory in biharmonic analysis 299
35. Sobolev imbeddings and integrability of harmonic functions on Holder domains 303
36. An estimate of harmonic measure with an application to subharmonic functions 315
37. Kuramochi boundaries of Riemannian manifolds 321
38. On axiomatic non-linear potential theory 331
39. The Neumann problem and Hausdorff measures 345
40. On potential extension and capacity on harmonic spaces 361
41. Singularities of the solution of integral equations of potential theory arising in problems of elasticity for non-homogeneous media 367
42. Appendices
43. List of participants 383
44. List of non-participating contributors 396
45. List of lectures 397
46. 404 404