Solvability of degenerate anisotropic elliptic second-order equations with L^1-data

In this article, we study the Dirichlet problem for degenerate anisotropic elliptic second-order equations with $L^1$-right-hand sides on a bounded open set of $mathbb{R}^n$ ($ngeqslant 2$). These equations are described with a set of exponents and of a set of weighted functions. The exponents characterize the rates of growth of the coefficients of the equations with respect to the corresponding derivatives of the unknown function, and the weighted functions characterize degeneration or singularity of the coefficients of the equations with respect to the spatial variable. We prove theorems on the existence of entropy solutions, T-solutions, W-solutions, and weighted weak solutions of the problem under consideration