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Kozlov V., Mazya V., Rossmann J. — Spectral problems associated with corner singularities of solutions to elliptic equations
Kozlov V., Mazya V., Rossmann J. — Spectral problems associated with corner singularities of solutions to elliptic equations

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Название: Spectral problems associated with corner singularities of solutions to elliptic equations

Авторы: Kozlov V., Mazya V., Rossmann J.

Аннотация:

This book focuses on the analysis of eigenvalues and eigenfunctions that describe singularities of solutions to elliptic boundary value problems in domains with corners and edges. The authors treat both classical problems of mathematical physics and general elliptic boundary value problems.
The volume is divided into two parts: The first is devoted to the power-logarithmic singularities of solutions to classical boundary value problems of mathematical physics. The second deals with similar singularities for higher order elliptic equations and systems.

Chapter 1 collects basic facts concerning operator pencils acting in a pair of Hilbert spaces. Related properties of ordinary differential equations with constant operator coefficients are discussed and connections with the theory of general elliptic boundary value problems in domains with conic vertices are outlined. New results are presented. Chapter 2 treats the Laplace operator as a starting point and a model for the subsequent study of angular and conic singularities of solutions. Chapter 3 considers the Dirichlet boundary condition beginning with the plane case and turning to the space problems. Chapter 4 investigates some mixed boundary conditions. The Stokes system is discussed in Chapters 5 and 6, and Chapter 7 concludes with the Dirichlet problem for the polyharmonic operator.

Chapter 8 studies the Dirichlet problem for general elliptic differential equations of order $2m$ in an angle. In Chapter 9, an asymptotic formula for the distribution of eigenvalues of operator pencils corresponding to general elliptic boundary value problems in an angle is obtained. Chapters 10 and 11 discuss the Dirichlet problem for elliptic systems of differential equations of order $2$ in an $n$-dimensional cone. Chapter 12 studies the Neumann problem for general elliptic systems, in particular with eigenvalues of the corresponding operator pencil in the strip $\mid {\Re} \lambda - m + /2n \mid \leq 1/2$. It is shown that only integer numbers contained in this strip are eigenvalues.

Applications are placed within chapter introductions and as special sections at the end of chapters. Prerequisites include standard PDE and functional analysis courses.


Язык: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 436

Добавлена в каталог: 15.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\kappa$-regular boundary conditions      297
Adjoint operator pencil      15
Admissible operator      27
Adolfsson, V.      58 417
Agmon, S.      31 255 320 344 417
Agranovich, M.S.      31 50 255 260 417
Algebraic multiplicity      11
Andersson, B.      59 138 417
Andrae, H.      138 419
Anisotropic elasticity      133 303 414
Apel, T.      219 417
Aronszajn, N.      389 417
Ashbaugh, M.S.      49 57 417
Aziz, A.K.      58 417
Babuska, I.      59 138 248 417 427
Bateman, H.      97 330 417
Bazant, Z.P.      105 132 138 417
Beagles, A.E.      59 105 417
Beltrami operator      40
Ben M'Barek      33 417
Benguria, R.D.      49 57 417
Benthem, J.P.      138 417
Biharmonic equation      227
Birman, M.Sh.      58 418
Blum, H.      248 418
Boersma, J.      58 418
Boussinesq, M.J.      97 176 418
Brown, S.N.      53 58 418
Bumb, H.      138 428
Canonical system      11
Capacity      43 90
Chavel, I.      57 418
Cherepanov, G.P.      105 123 418
Costabel, M.      105 138 291 418
Courant, R.      42 45 418
Dahlberg, B.E.J.      59 106 249 418
Dauge      29 32 58 105 138 196 290 345 418
Deny, J.      91 418
Deuring, P.      197 418
Dimitrov, A.      138 419
Dirichlet conditions      298
Donchev, T.      249 423
Douglis, A.      27 320 344 417 419
Eck, C.      138 419
Eigenvalue      10
Eigenvector      10
Energy line      17
Energy strip      17
Erdelyi, A.      97 330 417
Eskin, G.I.      31 32 291 419
Estenssoro, L.F.      138 417
Faber, G.      57 419
Fabes, E.B.      106 197 419
Falk, U.      138 417
Fichera, G.      58 59 419
Fourier transform      323 335
Fredholm operator      10
Friedland, S.      44 419
Fufaev, V.V.      58 419
Gantmakher, F.      265 270 419
Garding, L.      372
Gel'fand, I.M.      322 328 382 400 419
Gel'fond, O.A.      269 419
Generalized eigenvector      11
Generating function      66
Geometric multiplicity      10
Ghahremani, F.      138 419
Girault, V.      192 419
Gobert, J.      111 419
Gohberg, I.      12 13 32 67 419
Goldberg, S.      12 13 32 419
Green formula      377
Green function      104 194 313 358
Grisvard      29 58 105 138 197 248 291 419
Gromov, M.      32 420
Hanna, M.S.      58 420
Hayman, W.K.      44 419
Hilbert, D.      42 45 418
Hinder, R.      58 420
Holomorphic operator function      12
Hooke law      107 110 133
Hsiao, G.      138 420
Hussain, M.A.      138 426
Index of an eigenvalue      11
Index of an operator      29
Indicator      301
Inverse Fourier transform      339
Isoperimetric property      44 49 57
Jerison, D.      58 417 420
John, F.      313 317 344 420
Jordan chain      11
Kaashoek, M.A.      12 13 32 419
Kalex, H.-U.      225 420
Kato, T.      22 238 420
Keer, M.      105 132 417
Keldysh, M.V.      32 420
Keller, J.B.      58 420
Kellogg, R.B.      33 58 196 420 428
Kelvin transform      40 62 83 139 154
Kenig, C.E.      59 106 197 249 418 420
Komech, A.I.      58 291 421
Kondrat'ev, V.A.      29 31 58 106 248 291 387 421
Kopachek, I.      106 249 421
Kopasenko, V.V.      138 428
Korn's inequality      390
Kozlov, V.A.      13 29 32 58 105 138 178 197 225 248 291 305 344 387 417 421
Krahn, E.      57 422
Krasnosel'skii, M.A.      42 422
Kufner, A.      58 422
Ladyzhenskaya, O.A.      192 423
Lame system      61 385
Lancaster, P.      67 419
Landkof, N.S.      43 91 423
Laplace operator      36 40
Leading part of a differential operator      27
Leguillon, D.      33 138 423
Lemrabet, K.      33 423
Levin, A.V.      57 423
Levin, B.J.      301 423
Liebowitz, H.      105 423
Lions, J.-L.      35 91 225 418 423
Local coerciveness      389
Lopatinskii, Ya, B.      31 32 423
Lozi, R.      196 423
Magenes, E.      35 225 423
Magnus, W.      44 423
Malvern, L.E.      78 110 423
Markus, A.S.      32 423
Maslovskaya, L.V.      248 423
Maximum principle      104
Maz'ya, V.G.      13 29 32 43 45 52 57 105 138 142 178 194 197 199 225 247 289 344 384 387 389 417 422 427
Meister, E.      33 58 420 425
Mellin transform      9 356
Melrose, R.B.      32 425
Melzer, H.      248 425
Mennicken, R.      32 425
Merigot, M.      33 417
Merzon, A.E.      291 421
Mikhlin, S.G.      40 425
Miranda — Agmon maximum principle      247 249
Moeller, M.      32 425
Morozov, N.F.      248 423
Nadirashvili, N.S.      45 57 425
Nazarov, S.A.      29 32 52 58 138 290 344 384 387 419 423
Neumann conditions      298
Nicaise, S.      33 58 105 138 291 417 425
Nikishkin, V.A.      291 426
Nikol'skii, S.M.      58 426
Nirenberg, L.      27 31 255 320 344 417 419
Noble, B.      138 426
Oleinik, O.A.      32 106 249 421 426
Operator pencil      10
Orlt, M.      225 426
Osborn, J.E.      196 420 426
Parseval equality      356
Partial multiplicity      11
Parton, V.Z.      105 426
Pazy, A.      344 426
Penzel, F.      33 425
Perlin, P.I.      106 426
Pipher, J.      59 249 421 426
Plamenevskii, B.A.      29 32 52 58 105 142 194 197 199 247 289 344 384 387 423
Poisson kernel      307 320
Polyharmonic operator      228 239 329 384
Pu, S.L.      138 426
Rannacher, R.      248 418 425
Raviart, P.-A.      192 419
Regular boundary conditions      297
Regular point      10
Richter, U.      105 138 426
Rodman, L.      67 419
Rossmann, J.      29 32 58 138 225 248 290 387 422 425
Rouche's theorem      13
Saendig, A.-M.      33 58 105 138 225 417 425
Samarskii, A.A.      52 58 426
Sanchez-Palencia, E.      33 138
Schmitz, H.      59 138 426 428
Schnack, E.      138 419
Schulze, B.-W.      32 291 427
Schwab, C.      32 105 138 178 197 422
Seif, J.B.      248 427
Shapiro — Lopatinskii condition      297
Shaposhnikova, T.O.      59 425
Shen, C.L.      57 427
Shieh, C.T.      57 427
Shilov, G.E.      322 328 382 400 419
Shubin, M.A.      32 420 427
Sigal, E.I.      32 419 423
Simple eigenvalue      38
Skvortsov, G.E.      58 418
Smith, K.T.      58 420
Solonnikov, V.A.      58 199 225 320 344 42
Soni, R.P.      44 423
Speck, F.-O.      33 425
Spectrum      10
Sperner, E.      44 57 427
Spherical components      75
Spherical divergence      75
Spherical gradient      75
Stein, M.E.      330 427
Stephan, E.P.      59 138 420 427
Stewartson, K.      53 58 418
Stokes system      3 139 385
Strain tensor      107
Stress tensor      107
Strongly elliptic operator      309
Stupyalis, L.I.      199 225 424
Subspace of first kind      212
Subspace of second kind      212
Szabo, B.A.      248 427
Szego, G.      57 426 427
Tavkhelidze, I.N.      249 426
Teixeira, F.S.      33 425
Temam, R.      149 160 427
Trenogin, V.A.      124 270 282 427
Vainberg, M.M.      124 270 282 427
Variational Principle      42 91 119 168 221
Verchota, G.C.      106 197 249 418 426
Verzhbinskii, G.M.      58 427
Vishik, M.I.      31 50 255 260 417
Volk, K.      59 138 426
Volkov, E.A.      58 427 428
von Petersdorff, T.      59 138 417
Vorovich, I.I.      105 138 428
Walden, H.      59 428
Watson, G.N.      187 428
Weinberger, H.F.      50 57 426 428
Weiss, G.      330 427
Wendland, W.L.      32 59 138 419 426 428
Whiteman, J.R.      59 417 427
Whittaker, E.T.      187 428
Wigley, N.M.      58 428
Williams, M.L.      248 428
Yosifyan, G.A.      106 249 426
Zajaczkowski, W.      58 428
Zeidler, E.      42 428
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