Wolff potential estimates for elliptic obstacle problems with generalized Orlicz growth

2025/05/20 by Xiong, Qi, Fu, Xing
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.14089

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 C^1,α-regularity results for the solutions.

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