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

2025/09/18 by Picerni, Marco · 1 citation
#35B35 #35B45 #35B65 #35H20 #35J60 #35J70 #35R05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.14811

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 Poincaré 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.

Citations

• Existence, uniqueness, regularity and stability of solutions to linear X-elliptic equations with measurable coefficients
• Mean value formulas for classical solutions to some degenerate elliptic equations in Carnot groups
• Wiener criterion for X-elliptic operators

Cited by

• Regularizing effect of the interplay between coefficients in linear and semilinear X-elliptic equations

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