PDEA-seminarium: Green function estimates for nonlocal equations

Abstract:

We establish the optimal regularity for solutions to nonlocal elliptic equations with Hölder continuous coefficients in divergence form in bounded $C^{1,\alpha}$ domains. Our proof is based on a delicate higher order Campanato-type iteration at the boundary, which we develop in the context of nonlocal equations and which is quite different from the local theory. As an application of our results, we establish sharp two-sided Green function estimates for the same class of operators.

Detta är ett seminarium i vår seminarieserie om analys och partiella differentialekvationer (PDEA: The PDEs and Applications seminar).