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Abstract:In the present article we deal with the Dirichlet problem for a class of degenerate anisotropic elliptic second-order equations with L 1 -right-hand sides in a bounded domain of R n .n > 2/. This class is described by the presence of a set of exponents q 1 ; : : : ; q n and a set of weighted functions 1 ; : : : ; n in growth and coercitivity conditions on coefficients of the equations. The exponents q i characterize the rates of growth of the coefficients with respect to the corresponding derivatives of unknown function, and the functions i characterize degeneration or singularity of the coefficients with respect to independent variables. Our aim is to investigate the existence of entropy solutions of the problem under consideration.

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