Calderón–Zygmund type estimates for singular quasilinear elliptic obstacle problems with measure data
Volume 271 / 2023
Studia Mathematica 271 (2023), 287-319
MSC: Primary 35J87; Secondary 35B65, 35R06, 35J62, 35J75, 35J92.
DOI: 10.4064/sm220321-26-4
Published online: 26 June 2023
Abstract
We establish a Calderón–Zygmund type estimate for elliptic obstacle problems of $p$-Laplace type involving measure data under fractional maximal functions. Here, the problem is considered for the singular case when $1 \lt p\le 2-1/n$ and we prove the global regularity for weak solutions in the Lorentz spaces setting, under the assumption of small BMO coefficients and the domain being sufficiently flat in Reifenberg’s sense.
