Existence and regularity of solutions of some elliptic system in domains with edges

Zajączkowski, Wojciech M.

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Tytuł książki

Existence and regularity of solutions of some elliptic system in domains with edges

Autorzy

Wojciech M. Zajączkowski

Seria

Rozprawy Matematyczne tom/nr w serii: 274 wydano: 1988

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Abstrakty

CONTENTS
1. Introduction.......................................................................5
2. Notation and auxiliary results............................................9
3. Statement of the problem (1.1)-(1.3)..............................20
4. The problem (3.14).........................................................22
5. Auxiliary results in $D_ϑ$...............................................34
6. Existence of solutions of (3.14) in $H^k_μ(D_ϑ)$............41
7. Green function................................................................52
8. The problem (3.13) in $L^k_{p,μ}(D_ϑ)$ spaces............59
9. The problem (3.13) in weighted Hölder spaces...............67
10. The problem (1.1)-(1.3) in a bounded domain Ω..........75
Appendix. The distinguished case: μ+2/p∊ℤ......................86
References.........................................................................90

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Seria

Rozprawy Matematyczne tom/nr w serii: 274

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Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCLXXIV

Daty

wydano

1988

Twórcy

autor

Wojciech M. Zajączkowski

Polish Academy of Sciences, Institute of Fundamental Technology Research, Świętokrzyska 21, 00-049 Warsaw

Bibliografia

[1] E. B. Byhovsky, Solvability of mixed problem for the Maxwell equations for ideal conductive boundary, Vest. Len. Univ., Ser. Mat. Mekh. Astr. 13 (1957), 50-66 (in Russian).
[2] R. R. Coifman, C. Fefferman. Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 101(3) (1971), 241-250.
[3] D. M. Eidus, About existence of normal derivative of solution of the Dirichlet problem, Vest. Len. Univ. 13 (1956), 147-150 (in Russian).
[4] D. K. Faddeyev, V. A. Solonnikov, et al., Selected Topics of Analysis and Algebra, Isd. Len. Univ., Leningrad 1981 (in Russian).
[5] N. E. Kochin, Vectorial Calculus and Introduction to Tensor Calculus, Moscow 1951 (in Russian).
[6] V. A. Kondratiev, About smoothness of solutions of the Dirichlet problem for elliptic equations of second order in domains with sectionally smooth boundary, Diff. Uravn. 6 (1970), 1831-1843 (in Russian).
[7] V. A. Kondratiev, Boundary value problems,for elliptic equations in domains with conical and angular points, Trudy Mosk. Mat. Obshch. 16(1967), 209-292 (in Russian).
[8] O. A. Ladyzhenskaya, Boundary Value Problems for Mathematical Physics, Moscow 1973 (in Russian).
[9] O. A. Ladyzhenskaya, N. N. Uraltzeva, Linear and Quasilinear Equations of Elliptic Type, Moscow 1973 (in Russian).
[10] V. G. Maz'ya, B. A. Plamenevsky, $L_p$ estimates for elliptic boundary value problems in domains with edges, Trudy Mosk. Mat. Obshch. 37(1978), 49-93 (in Russian).
[11] V. G. Maz'ya, B. A. Plamenevsky, Estimates in $L_p$ and in Hölder spaces and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary, Math. Nachr. 81(1978), 25-82 (in Russian).
[12] V. G. Maz'ya, B. A. Plamenevsky, About coefficients in asymptotic of solutions of elliptic boundary value problems in domains with conical points, Math. Nachr. 76(1977), 29-60 (in Russian).
[13] V. A. Solonnikov, W. M. Zajączkowski, About the Neumann problem for elliptic equations of second order in domains with edges on boundary, Zap, Nauch. Sem. LOMI 127(1983), 7-48 (in Russian).
[14] V. A. Solonnikov, Estimates for solutions of the Neumann problem for elliptic equations of second order in domains with edges on boundary, Preprint LOMI, P-4-83, 1983 (in Russian).
[15] V. A. Solonnikov, Overdetermined elliptic boundary value problems, Zap. Nauch. Sem. LOMI 21(1971), 112-158 (in Russian),
[16] V. A. Solonnikov, Solvability of three-dimensional problem with a free boundary for the stationary system of Navier-Stokes equations. Zap. Nauch. Sem. LOMI 84(1979), 252-285 (in Russian).
[17] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, New Jersey, 1970.
[18] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Berlin 1978.
[19] P. Urbański, Dirichlet type boundary value problems in magnetostatics, to appear.
[20] W. M. Zajączkowski, On theorem of embedding for weighted Sobolev spaces, Bull. Pol. Acad. Sc., Ser. Math. 32(3-4) (1985), 115-121.

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bwmeta1.element.zamlynska-17687504-7d2d-4184-a9c0-699d54475e91

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83-01-08767-6

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0012-3862

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