Gradient estimates for singular p-Laplace type equations with measure data

We are concerned with interior and global gradient estimates for solutions to a class of singular quasilinear elliptic equations with measure data, whose prototype is given by the p-Laplace equation −Δp​u=μ with p∈(1,2). The cases when p∈(2−n1​,2) and p∈(2n−13n−2​,2−n1​] were studied in Duzaar and Mingione [J. Funct. Anal. 259 (2010), 379–418] and Nguyen and Phuc [J. Funct. Anal. 278 (2020), art. 108391] respectively. In this paper, we improve the results of Nguyen and Phuc and address the open case when p∈(1,2n−13n−2​]. Interior and global modulus of continuity estimates of the gradients of solutions are also established.

Duke Scholars

Author Hanye Zhu Mathematics