Gradient potential estimates in elliptic obstacle problems with Orlicz growth

2021/04/01 by Qi, Xiong, Zhang, Zhenqiu, Ma, Lingwei · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.00260

Abstract

In this paper,we consider the solutions of the non-homogeneous elliptic obstacle problems with Orlicz growth involving measure data. We first establish the pointwise estimates of the approximable solutions to these problems via fractional maximal operators. As a result, we obtain pointwise and oscillation estimates for the gradients of solutions by the non-linear Wolff potentials, and these yield results on C^1,α-regularity of solutions.

Cited by

• Universal Potential Estimates for Mixed Local and Nonlocal Nonlinear Measure Data Problems

Related

• Gradient potential estimates for elliptic double obstacle problems with Orlicz growth
• Wolff potential estimates for elliptic obstacle problems with generalized Orlicz growth
• Riesz potential estimates for double obstacle problems with Orlicz growth
• Riesz potential estimates for non-linear elliptic obstacle problems
• Weighted distribution approach to gradient estimates for quasilinear elliptic double-obstacle problems in Orlicz spaces