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arXiv · 2509.14811

Existence and summability of solutions to nonlinear X-elliptic equations with measurable coefficients

Marco Picerni
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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.

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Marco Picerni. 2025-09-18. Existence and summability of solutions to nonlinear X-elliptic equations with measurable coefficients. https://doi.org/10.1007/s10231-026-01667-3

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