Geodesic
Some auxiliary estimates for solutions to non-uniformly degenerate second-order elliptic equations
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 1, pp. 23-30

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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. 
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     author = {S. T. Huseynov and M. J. Aliyev},
     title = {Some auxiliary estimates for solutions to non-uniformly degenerate second-order elliptic equations},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
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S. T. Huseynov; M. J. Aliyev. Some auxiliary estimates for solutions to non-uniformly degenerate second-order elliptic equations. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 1, pp. 23-30. http://geodesic.mathdoc.fr/item/VSGU_2024_30_1_a1/