We will discuss recent results on gradient estimates for solutions to singular quasilinear elliptic (or parabolic) equations with measure data, whose prototype is given by the elliptic (or parabolic) $p$-Laplace equation $-\Delta_p u=\mu$ (or $u_t-\Delta_p u=\mu$) with $p\in(1,2)$. For these singular nonlinear equations, we obtain pointwise gradient estimates via linear elliptic (or parabolic) Riesz potential and gradient continuity results via certain assumptions on the linear Riesz potential. This is based on joint works with Hongjie Dong.

https://arizona.zoom.us/j/82763762677