Weyl's lemma on RCD(K, N) metric measure spaces.

Peng, Yu; Zhang, Hui-Chun; Zhu, Xi-Ping

In this paper, we extend the classical Weyl's lemma to RCD(K, N) metric measure spaces. As its applications, we show the local regularity of solutions for Poisson equations and a Liouville-type result for L 1 very weak harmonic functions on RCD(K, N) spaces. Meanwhile, as an application of regularity theory on non-smooth settings, we obtain a gradient estimate for solutions to a class of elliptic equations with discontinuous coefficients.

METRIC spaces; DISCONTINUOUS coefficients; SET theory; EQUATIONS

Calculus of Variations & Partial Differential Equations, 2025, Vol 64, Issue 1, p1

0944-2669

Academic Journal

10.1007/s00526-024-02862-x