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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

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}