Title: Existence and summability of solutions to nonlinear X-elliptic equations with measurable coefficients Show Chinese title

Title: 具有可测系数的非线性X-椭圆方程解的存在性和可和性

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. Show Chinese abstract

Abstract: 我们证明了一类具有可测系数和零狄利克雷边界条件的非线性退化椭圆方程解的存在性结果。 主要项是由满足Poincaré不等式和倍增条件的向量场族相关联的散度形式的非线性算子给出的。 此外，我们证明解满足$L^p$-正则性结果的推广，这些结果适用于Leray-Lions型方程的解。