Special Session 55: Nonlocal effects in diffusion equations

A study on the regularity of mixed local-nonlocal problems with measure data
Mengyao Ding
Harbin institute of Technology
Peoples Rep of China
Co-Author(s):    YingLi, ChaoZhang
Abstract:
We investigate the existence, uniqueness, and regularity of solutions in the framework of fractional Sobolev spaces for mixed local-nonlocal problems with measure data. By combining techniques from the theory of linear elliptic equations with nonlocal operators and classical potential theory, we derive some regularity estimates for the equation.