國立清華大學 數學系

Abstract:
The Aleksandrov-Bakelman-Pucci (ABP) Maximum Principle is a pointwise estimate in elliptic PDE theory. From this estimate, One can achieve Hölder regularity of solution. In this talk I will talk about nonlocal version of ABP estimate on some manifolds. We will briefly review classical PDE regularity theory on both divergent and non-divergent form. After that, I will introduce nonlocal elliptic ABP estimate on Euclidean space and on some manifolds. Also, I would like to introduce nonlocal divergent (Dirichlet form) case and some geometric condition.