[GS_M_APP] Partial differential equations in weighted Sobolev spaces
ABSTRACT
In this talk, we discuss two types of equations in weighted Sobolev spaces. First, we present degenerate equations on the upper half space. The coefficient matrices of the equations are the product of $x_d^2$ and bounded uniformly elliptic matrices. Next, we consider nonlocal equations on $C^{1,\tau}$ open sets where $\tau\in(0,1)$. The operators we consider are infinitesimal generators of symmetric stable L\'evy processes, whose L\'evy measures are allowed to be very singular. This talk is based on joint works with Jae-Hwan Choi, Kyeong-Hun Kim, and Hongjie Dong.