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 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]: Year: Volume: Issue: Page: Find

 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011, Issue 1(22), Pages 53–67 (Mi vsgtu936)

Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Mathematical Physics

The estimates of the solution of the Dirichlet problem with boundary function from $L_p$ for a second-order elliptic equation

A. K. Gushchin

Dept. of Mathematical Physics, Steklov Mathematical Institute, Russian Academy of Sciences, Moscow

Abstract: We study the solvability of the Dirichlet problem for a second-order elliptic equation with measurable and bounded coefficients. Assuming that coefficients of equation are Dini-continued on the boundary, it is established that there is the unique solution of the Dirichlet problem with boundary function from $L_p$, $p>1$. We prove the estimate of the analogue of area integral.

Keywords: elliptic equation, Dirichlet problem, functional space

DOI: https://doi.org/10.14498/vsgtu936

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Bibliographic databases:

UDC: 517.956.2
MSC: Primary 35D05; Secondary 35J25, 35B30, 35R05, 35B45
Original article submitted 20/XII/2010
revision submitted – 27/III/2011

Citation: A. K. Gushchin, “The estimates of the solution of the Dirichlet problem with boundary function from $L_p$ for a second-order elliptic equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 53–67

Citation in format AMSBIB
\Bibitem{Gus11}
\by A.~K.~Gushchin
\paper The estimates of the solution of the Dirichlet problem with boundary function from $L_p$ for a~second-order elliptic equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 1(22)
\pages 53--67
\mathnet{http://mi.mathnet.ru/vsgtu936}
\crossref{https://doi.org/10.14498/vsgtu936}
\elib{https://elibrary.ru/item.asp?id=16387159}