Continuity estimates for solutions to nonlocal equations
Abstract
Regularity theory is a core topic in the analysis of differential and integro-differential equations. This talk will focus on regularity estimates for solutions to a class of integro-differential equations with highly singular and non-smooth kernels. First, I will present results for operators with a fixed order of differentiability between zero and two. Then, I will show how to establish boundedness and regularity estimates for weak solutions to linear nonlocal equations with integro-differential operators that have almost no order of differentiability. Finally, I will discuss two open problems in this area that are accessible to a broad mathematical audience. This work is based on joint results with M. Weider, as well as recent research with S. Jarohs and T. Weth.
