Boundary value problems, integral equations and related problems. 3 conf.

Contents......Page 8
Preface......Page 6
1. Introduction......Page 13
2. Preliminaries......Page 14
3. Construction of an Approximate Solution and a Priori Estimates......Page 15
4. Existence of a Generalized Solution......Page 18
References......Page 23
1. Formulation of Oblique Derivative Problems......Page 24
2. Estimates of Solutions of Oblique Derivative Problems......Page 28
3. Solvability of Oblique Derivative Problems......Page 30
References......Page 33
1. Introduction......Page 34
2.1. Definitions, statements of theorems......Page 37
2.3. Proofs of theorems......Page 45
3. Heat Bounded Functions and the Heat Equation......Page 57
4. Applications to the Navier-Stokes Equation......Page 60
References......Page 62
CHARACTERIZATION OF THE SPECTRUM OF AN IRREGULAR BOUNDARY VALUE PROBLEM FOR THE STURM-LIOUVILLE OPERATOR......Page 64
References......Page 69
1. Introduction......Page 70
2. The Exterior Tricomi Problem......Page 71
3. Open Problems......Page 81
References......Page 82
1. Formulation of the Riemann-Hilbert Problem for Degenerate Elliptic Complex Equations......Page 84
2. Representations and Estimates of Solutions of the Riemann-Hilbert Problem for Elliptic Complex Equations......Page 86
3. Solvability of the Riemann-Hilbert Problem for Degenerate Elliptic Complex Equations......Page 91
References......Page 93
1. Formulation of Discontinuous Oblique Derivative Problems for Second Order Mixed Equations......Page 94
2. Representation of Solutions for Discontinuous Oblique Derivative Problems for Second Order Mixed Equations......Page 98
3. Solvability of Discontinuous Oblique Derivative Problems for Second Order Mixed Equations......Page 100
References......Page 103
2. Notation and Definitions......Page 104
3. Proof of the Trilinear Estimate......Page 105
4. Local Well-Posedness for 4NLS Equation......Page 111
References......Page 113
1. Introduction......Page 114
2. Volatility Calibration of Exponential Iévy Model Using a Relative Entropy Regularization Method......Page 115
3. Choice of the Regularization Parameter......Page 118
4. Method for Minimizing J(v)......Page 120
5. Numerical Algorithm......Page 121
7. Conclusion......Page 122
References......Page 123
1. Background for Textile Material Design......Page 125
2. Mathematical Model of Heat and Mass Transfer......Page 126
4. Thickness Design of Textile Materials Under Low Temperature......Page 127
5. Regularized Solution of the IP 1......Page 128
6. Iteration Algorithms of the Regularized Solution......Page 129
7. Type Design of Textile Materials Under Low Temperature......Page 130
9. Iteration Algorithms of the Regularized Solution......Page 131
10. Numerical Solution......Page 132
References......Page 133
1. Formulation of Inverse Problem for Elliptic Complex Equations of First Order......Page 134
2. Existence of Solutions of Inverse Problem for Elliptic Complex Equations of First Order......Page 136
3. Inverse Problem for Second Order Elliptic Equations from Dirichlet to Neumann Map......Page 141
References......Page 143
1. Introduction......Page 144
2. Some Preliminaries......Page 145
3. Numerical Inversion......Page 146
References......Page 150
1. Introduction......Page 152
2. The Regularization Method and Main Results......Page 154
3. The Proof of Theorems......Page 156
References......Page 164
1. Introduction......Page 166
2. The Gradient Regularization Method......Page 168
3. Projection......Page 170
5. Conclusion......Page 171
References......Page 173
1. Introduction and Statement of Result......Page 175
2. Preliminary Lemmas......Page 177
3. Proof of Theorem......Page 178
References......Page 180
1. Introduction and Statement of Result......Page 182
2. Some Notations......Page 184
3. Some Lemmas......Page 185
4. Proof of Theorem 1.1......Page 189
References......Page 190
1. Introduction......Page 191
2. Proof of Theorem 1.1......Page 193
References......Page 197
1. Introduction......Page 198
2. Differential Forms on Riemannian Manifolds......Page 200
3. (K1,K2)-Quasiregular Mappings......Page 202
References......Page 206
1. Introduction......Page 207
2. Proof of Theorem 1.1......Page 210
(1) Lipschitz condition......Page 212
(3) Homogeneity condition......Page 213
References......Page 216
1. Introduction......Page 217
2. Preliminary Knowledge and Lemmas......Page 219
3. Proof of Theorem A......Page 220
4. Proof of Theorem B......Page 225
References......Page 226
1. Introduction and Main Results.......Page 227
2. The Palais-Smale Condition......Page 229
3. Proof of Theorem 1.1......Page 234
References......Page 235
1. Introduction......Page 237
2. Preliminaries......Page 238
3. Characterizations for Mappings in MHp (α)∩T1 and MHp (α)∩T2......Page 243
4. Starlikeness and Convexity of P-Harmonic Mappings......Page 245
References......Page 246
1. Clifford Algebra Cln and Regular Function......Page 248
2.1 Hypermonogenic function......Page 249
2.6 The uniqueness theorem of hypermonogenic function......Page 250
2.7 Cauchy integral formula and Plemelj formula for bihyper-monogenic functions......Page 251
3.3 Cauchy integral formula of k-holomorphic function......Page 252
3.4 Boundary behavior of higher order Cauchy-type integrals over unbounded domain......Page 254
References......Page 255
2. Integral Representation for K-Regular Functions......Page 256
3. Privalov Theorem and Plemelj Formula......Page 259
References......Page 265
1. Introduction......Page 266
2. Preliminaries and Dunkl Analysis......Page 267
3. Proof of the Main Theorem......Page 270
References......Page 272
2 Preliminaries......Page 273
3 The Left Linear Hilbert Problem......Page 276
References......Page 281
MODIFIED HELMHOLTZ EQUATION AND H-REGULAR VECTOR FUNCTION1......Page 282
1. Some Notations and Definitions......Page 283
2. Pompeiu Formula and Cauchy Integral Formula of Hλ-Regular Vector Function......Page 284
3. Cauchy Type Integral and Plemelj Formula......Page 286
4. Operator TΩf......Page 289
References......Page 291
1. Introduction......Page 292
(1) The investigations of static and dynamic crack problems in FGCMs (Non-periodic cases)......Page 293
(2) The investigations of static and dynamic crack problems in FGCMs (Periodic cases)......Page 295
3. IEM for Scattering of SH Wave of Functionally Graded Piezoelectric/Piezomagnetic Materials......Page 296
4. Thermal Elastic Fracture Analysis of FGMs......Page 297
5. Contact Problem of FGMs......Page 298
References......Page 299
1. Introduction......Page 301
2. Formulation of the Problem......Page 302
3. Numerical Results and Discussion......Page 306
References......Page 308
Appendix......Page 309
1. Basic Knowledge and Notations......Page 312
2. Nöether's Theory of Some Two-Dimensional Singular Integral Operator with Continuous Coefficients......Page 314
3. Applications of Nöether's Theory in Second Order Elliptical Equations......Page 318
References......Page 320
1. Introduction, Definitions and Preliminaries......Page 321
2. Coefficient Inequalities for Classes Um, n(α, A, B) and Vsm,n(α,A, B)......Page 324
3. Integral Mean Inequalities......Page 325
4. Subordination Result......Page 328
References......Page 331
1. The Fundamental Problems in Plane Elasticity......Page 333
2. The Stability of the Perturbed First Fundamental Problem......Page 334
3. The Stability of the Perturbed Second Fundamental Problem......Page 336
References......Page 338
1. Introduction......Page 339
2. Derivation of the Problem and the Non-uniform FDM......Page 340
3. Convergence Result......Page 341
4. Numerical Example......Page 343
5. Stability Analysis......Page 346
References......Page 349
1. The Fast Multiscale Galerkin Method for Lavrentiev Regularization......Page 350
2. Error Estimate......Page 353
3. Regularization Parameter Choice Strategies......Page 356
4. Convergence Rate Analysis......Page 358
References......Page 360
1. Introduction......Page 361
2. Problem Transformation......Page 363
3. The Approximate Solution of the Elliptic Problem......Page 365
4. Error Estimates of the Approximate Solution......Page 367
References......Page 369
2. Materials and Definitions......Page 370
3. Finite Difference Method......Page 372
4. Stability of Fuzzy Heat Equation......Page 375
5. Numerical Example......Page 377
References......Page 379
1. Introduction......Page 380
2. The Finite Difference Schemes......Page 381
3. Numerical Example......Page 384
References......Page 385
1. Formulation of the Problem......Page 386
2. Green's Function......Page 388
3. Example of a Solution......Page 389
References......Page 391
1. Introduction......Page 392
2. Preliminaries......Page 394
3. Proof of Main Theorem......Page 395
References......Page 398
1. Introduction......Page 400
2. The Main Results and Its Proof......Page 401
References......Page 403
1. Introduction......Page 404
2. Main Results......Page 405
References......Page 409
1. Introduction......Page 411
2. Proof of the Main Theorem......Page 417
References......Page 419
1. Introduction......Page 420
2. Lemma and Preliminary Knowledge......Page 422
3. Theorem and Its Proof......Page 423
References......Page 425
2.1. Product spaces......Page 426
2.2. Integrals......Page 430
3.1. Manifolds......Page 431
3.3. The principal value......Page 432
3.4. Plemelj formulas......Page 433
4. Riemann Boundary Value Problems......Page 434
References......Page 435