Gradient estimates for $p\left(\cdot\right)$-harmonic differential forms
偏微分方程分析
2026-05-22 v1
摘要
In this paper, we establish gradient bounds for -harmonic differential forms subject to a Coulomb-type gauge condition. For variable exponents satisfying the log-H\"older continuity assumption, we derive higher integrability estimates of Meyers type, ensuring improved regularity beyond the natural energy space. Furthermore, under the stronger assumption of H\"older continuity of the exponent function, we prove that the gradient of solutions exhibits H\"older continuity. These results extend classical regularity theory for constant-exponent -harmonic systems to the variable-exponent setting, which is essential for modeling nonhomogeneous and anisotropic media.
引用
@article{arxiv.2605.22178,
title = {Gradient estimates for $p\left(\cdot\right)$-harmonic differential forms},
author = {Anna Balci and Swarnendu Sil and Mikhail Surnachev},
journal= {arXiv preprint arXiv:2605.22178},
year = {2026}
}