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Vestnik Samarskogo Universiteta. Estestvenno-Nauchnaya Seriya, 2024, Volume 30, Issue 1, Pages 23–30
DOI: https://doi.org/10.18287/2541-7525-2024-30-1-23-30
(Mi vsgu725)
 

Mathematics

Some auxiliary estimates for solutions to non-uniformly degenerate second-order elliptic equations

S. T. Huseynov, M. J. Aliyev

Baku State University, Baku, Republic of Azerbaijan (published under the terms of the Creative Commons Attribution 4.0 International License)
References:
Abstract: We consider a class of second order elliptic equations in divergence form with non-uniform exponential degeneracy. The method used is based on the fact that the degeneracy rates of the eigenvalues of the matrix $|| a_{ij}(x)||$ (function $\lambda_i(x)$) are not the functions of unusual norm $|x|$, but of some anisotropic distance $| x|_{{a}^{-}}$. We assume that the Dirichlet problem for such equations is solvable in the classical sense for every continuous boundary function in any normal domain $\Omega$.
Estimates for the weak solutions of Dirichlet problem near the boundary point are obtained, and Green's functions for second order non-uniformly degenerate elliptic equations are constructed.
Keywords: uniform ellipticity, non-uniform degeneration spaces, fundamental solution.
Received: 15.01.2024
Revised: 19.02.2024
Accepted: 28.02.2024
Document Type: Article
UDC: 517.956
Language: Russian
Citation: S. T. Huseynov, M. J. Aliyev, “Some auxiliary estimates for solutions to non-uniformly degenerate second-order elliptic equations”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 30:1 (2024), 23–30
Citation in format AMSBIB
\Bibitem{HusAli24}
\by S.~T.~Huseynov, M.~J.~Aliyev
\paper Some auxiliary estimates for solutions to non-uniformly degenerate second-order elliptic equations
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2024
\vol 30
\issue 1
\pages 23--30
\mathnet{http://mi.mathnet.ru/vsgu725}
\crossref{https://doi.org/10.18287/2541-7525-2024-30-1-23-30}
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    Вестник Самарского государственного университета. Естественнонаучная серия
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