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Mat. Sb. (N.S.), 1985, Volume 128(170), Number 3(11), Pages 429–445 (Mi msb2169)  

Unimprovable estimates in Hölder spaces for generalized solutions of the Dirichlet problem for a class of fourth order elliptic equations

D. M. Lekveishvili


Abstract: Generalized solutions of the Dirichlet problem for a fourth order elliptic equation in two independent variables are investigated. Unimprovable estimates are obtained for the modulus of the generalized solution and its first derivatives in the neighborhood of a boundary point; it is also proved that the generalized solutions belong to a Hölder space with an unimprovable index depending on the geometry of the domain.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 56:2, 429–446

Bibliographic databases:

UDC: 517.956
MSC: Primary 35J40, 35D10, 35B45; Secondary 73K10
Received: 24.09.1984

Citation: D. M. Lekveishvili, “Unimprovable estimates in Hölder spaces for generalized solutions of the Dirichlet problem for a class of fourth order elliptic equations”, Mat. Sb. (N.S.), 128(170):3(11) (1985), 429–445; Math. USSR-Sb., 56:2 (1987), 429–446

Citation in format AMSBIB
\Bibitem{Lek85}
\by D.~M.~Lekveishvili
\paper Unimprovable estimates in H\"older spaces for generalized solutions of the Dirichlet problem for a~class of fourth order elliptic equations
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 128(170)
\issue 3(11)
\pages 429--445
\mathnet{http://mi.mathnet.ru/msb2169}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=815274}
\zmath{https://zbmath.org/?q=an:0662.35005|0597.35011}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 2
\pages 429--446
\crossref{https://doi.org/10.1070/SM1987v056n02ABEH003045}


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