Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 167, pp. 1-17.

Title: Solvability of degenerate anisotropic elliptic
       second-order equations with $L^1$-data
        
Authors: Alexander A. Kovalevsky (National Academy of Sciences, Donetsk, Ukraine)
         Yuliya S. Gorban (Donetsk National Univ., Donetsk, Ukraine)

Abstract:
 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 $\mathbb{R}^n$  ($n\geqslant 2$).
 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.

Submitted November 28, 2012. Published July 22, 2013.
Math Subject Classifications: 35J25, 35J60, 35J70, 35R05.
Key Words: Degenerate anisotropic elliptic second-order equations;
    L1-data; Dirichlet problem; entropy solution; T-solution;
    W-solution; weighted weak solution; existence of solutions.