Recent advances on elliptic and parabolic issues: Proc. of Swiss-Japanese seminar

Michel Chipot, Hirokazu Ninomiya9812566759, 9789812566751, 9789812774170

Table of contents :
CONTENTS……Page 8
Preface……Page 6
1 Introduction……Page 10
2 The semi-infinite vertical flat plate case……Page 11
3 A model problem in a bounded domain……Page 14
4 Conclusion……Page 23
References……Page 24
1 Introduction……Page 28
2 Model problems……Page 30
3 Parameter dependent evolution equations……Page 38
4 Functional evolution equations……Page 42
5 Parabolic boundary value problems……Page 45
6 Proofs for the model problems……Page 49
References……Page 51
1 Introduction……Page 54
2 Main existence results……Page 57
3 Qualitative properties of eigenfunctions……Page 64
4 Spectral theory……Page 70
5 Eigenvalues in the resonance case……Page 78
References……Page 85
1 Local versus nonlocal……Page 88
2 Nonlocal problems as the limit of local ones……Page 90
3 Simple existence result……Page 95
4 Nonlocal problems in the calculus of variations……Page 97
5 A class of intermediate problems……Page 104
References……Page 111
1 Introduction……Page 112
2 Notations and preliminaries……Page 114
3 Generalized notions of convexity……Page 117
4 Separation results for polyconvex sets……Page 122
5 Generalized convex hulls……Page 123
6 Extreme points……Page 131
References……Page 136
1 Introduction……Page 138
2 Convex case……Page 141
3 An example of degenerate pinching singularity in nonconvex case……Page 146
References……Page 150
1 Introduction……Page 154
2 Modification of equations……Page 159
3 Proof……Page 161
References……Page 172
1 Introduction……Page 174
2 Transformation to the exterior problem……Page 179
3 Structure of solutions to the exterior problem……Page 184
4 Critical exponent case……Page 187
5 Three dimensional case……Page 189
6 Higher dimensional case……Page 191
7 Related topics……Page 196
References……Page 197
1 Introduction……Page 200
2 Main result……Page 202
3 Lower estimate of the functional……Page 206
4 Proof of the theorem……Page 223
5 References……Page 225
1 Introduction……Page 228
2 Formal derivation of the singular limit……Page 229
3 Main result……Page 232
4 Generation of interface……Page 234
5 Proof of Theorem 4.1……Page 236
6 Motion of interface……Page 244
7 Proof of Theorem 1……Page 247
References……Page 248
1 Introduction……Page 250
2 The Rayleigh Benard problem……Page 251
3 2-D problem and stability of mixed mode solutions……Page 254
4 3-D problem……Page 260
References……Page 273
1 Introduction……Page 274
2 Convergence in the linear case……Page 275
3 Convergence in some nonlinear cases……Page 285
References……Page 291
2 Definitions……Page 292
3 Existence of global unbounded solutions……Page 295
4 Grow-up rate……Page 296
5 Grow-up set……Page 299
References……Page 300