Existence, uniqueness, regularity and stability of solutions to linear X-elliptic equations with measurable coefficients

2025/06/18 by Marco Picerni, Picerni, Marco · 2 citations
#35B35 #35B45 #35B65 #35H20 (Primary) 35J70 #35R05 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.15409

Abstract

We prove an existence and uniqueness result for solutions to linear X-elliptic equations with L¹ data and zero Dirichlet boundary conditions. Such solutions depend continuously on the datum. Moreover, we show that an improvement in the summability of the data yields a corresponding improvement in the summability of the solutions, in a manner analogous to the one that occurs in the case of uniformly elliptic equations.

Citations

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

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