Wolff potential estimates for elliptic obstacle problems with generalized Orlicz growth
Analysis of PDEs
2025-05-21 v1
Abstract
This paper investigates elliptic obstacle problems with generalized Orlicz growth involving measure data, which includes Orlicz growth, variable exponent growth, and double-phase growth as specific cases of this setting. First, we establish the existence of solutions in the Musielak-Orlicz space. Then, we derive pointwise and oscillation gradient estimates for solutions in terms of the non-linear Wolff potentials, assuming minimal conditions on the obstacle. These estimates subsequently lead to -regularity results for the solutions.
Cite
@article{arxiv.2505.14089,
title = {Wolff potential estimates for elliptic obstacle problems with generalized Orlicz growth},
author = {Qi Xiong and Xing Fu},
journal= {arXiv preprint arXiv:2505.14089},
year = {2025}
}