Vlll
CONTENTS
5.1. Operator-valued polynomials and applications to ordinary differential
equations with operator coefficients 145
5.2. Solvability of the model problem in an infinite cylinder 153
5.3. Solvability of the model problem in the cylinder in Sobolev spaces of
negative order 161
5.4. Asymptotics of the solution of the model problem at infinity 168
5.5. The boundary value problem with coefficients which stabilize at infinity 180
Chapter 6. Elliptic boundary value problems in domains with conical points 191
6.1. The model problem in an infinite cone 191
6.2. Elliptic boundary value problems in a bounded domain with conical
points 212
6.3. Solvability of elliptic boundary value problems in bounded domains
with conical points 219
6.4. Asymptotics of the solution 234
6.5. Boundary value problems with parameter in domains with conical
points 246
6.6. Examples 260
Chapter 7. Elliptic boundary value problems in weighted Sobolev spaces with
nonhomogeneous norms 267
7.1. Relations between weighted Sobolev spaces 267
7.2. Elliptic problems in spaces with nonhomogeneous norms 277
7.3. Weighted Sobolev spaces with critical value of the weight parameter 286
Chapter 8. Variants and extensions 303
8.1. Elliptic problems with boundary operators of higher order in bounded
domains with conical points 303
8.2. Elliptic problems for systems of differential equations 309
8.3. Boundary value problems in the variational form 315
8.4. Further results 322
8.5. Notes 332
Part 3. Elliptic problems in domains with cuspidal points 335
Chapter 9. Elliptic boundary value problems in domains with exterior cusps 337
9.1. Elliptic boundary value problems in quasicylindrical domains 337
9.2. Elliptic boundary value problems in cuspidal domains 346
9.3. Variants and extensions 349
9.4. Further results 354
9.5. Notes 356
Chapter 10. Elliptic boundary value problems in domains with inside cusps 357
10.1. Formulation of the problem 358
10.2. The first limit problem 362
10.3. The second limit problem 369
10.4. The auxiliary problem 377
10.5. Elliptic problems in domains of the exterior of a cusp type 388
10.6. Notes 396
Bibliography
397
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