Some auxiliary estimates for solutions to non-uniformly degenerate second-order elliptic equations - Sarvan T. Huseynov; Mushfig J. Aliyev (Вестник Самарского университета: Естественнонаучная серия)
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 ||aij(x)||(function λi(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 Ω.