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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)
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
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
Linking options:
https://www.mathnet.ru/eng/vsgu725 https://www.mathnet.ru/eng/vsgu/v30/i1/p23
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Abstract page: | 40 | Full-text PDF : | 14 | References: | 21 |
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