Gradient Riesz potential estimates for a general class of measure data quasilinear systems

2023/07/28 by Chlebicka, Iwona, Kim, Minhyun, Weidner, Marvin
#35B45 #35J47 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.15525

Abstract

We study the gradient regularity of solutions to measure data elliptic systems with Uhlenbeck-type structure and Orlicz growth. For any bounded Borel measure, pointwise estimates for the gradient of solutions are provided in terms of the truncated Riesz potential. This allows us to show a precise transfer of regularity from data to solutions on various scales.

Related

• Wolff potentials and measure data vectorial problems with Orlicz growth
• Gradient potential estimates in elliptic obstacle problems with Orlicz growth
• Riesz potential estimates for mixed local-nonlocal problems with measure data
• Gradient estimates via Riesz potentials and fractional maximal operators for quasilinear elliptic equations with applications
• Global gradient estimates for very singular quasilinear elliptic equations with measure data