Anal. PDE 15 (8), 1879-1895, (2022) DOI: 10.2140/apde.2022.15.1879
Quoc-Hung Nguyen, Nguyen Cong Phuc
KEYWORDS: quasilinear equation, Riccati-type equation, measure data, good-λ inequality, Muckenhoupt–Wheeden-type inequality, weighted norm inequality, capacity, 35J60, 35J61, 35J62, 35J75, 42B37
We obtain existence and global regularity estimates for gradients of solutions to quasilinear elliptic equations with measure data whose prototypes are of the form in a bounded domain potentially with nonsmooth boundary. Here either or , is a finite signed Radon measure in , and . Our main concern is to extend earlier results to the strongly singular case . In particular, in the case which corresponds to a Riccati-type equation, we settle the question of solvability that has been raised for some time in the literature.