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Abstract

We prove an existence result for solutions to a class of nonlinear degenerate-elliptic equations with measurable coefficients and zero Dirichlet boundary condition. The main term is given by a nonlinear operator in divergence form associated to a family of vector fields which satisfy a Poincar\'e inequality and the doubling condition. Furthermore, we prove that the solutions satisfy a generalization of the $L^p$-regularity results which hold for the solutions to Leray-Lions type equations.