A Geometric Proof for Interior $L^p$ Estimates of a Class of Non-Local Elliptic Equations
Time: 2019-05-10
Published By: Ningbo Lu
Speaker(s): Yi CAO (Shaanxi Normal University)
Time: 08:30-10:30 May 26, 2019
Venue: Room 29, Quan Zhai, BICMR
Abstract:
In this talk, I will discuss our work on the interior $L^p$ estimates to a class of non-local elliptic equations with kernels $K(x,y)=a(x,y)/|y|^{n+\sigma}$ $(\sigma\in(0,2))$ in a bounded domain by a geometric method, where functions $a(.,y)$ are uniformly bounded and equicontinuous on the variable $y$. Our results generalize the classical Calderon-Zgymund estimates. The analytical tools used in this paper are Hardy-Littlewood maximum functions, energy estimates and Besicovich’s covering lemma. The main difficulty in proving these results is that the kernels are non-local.
In this talk, I will discuss our work on the interior $L^p$ estimates to a class of non-local elliptic equations with kernels $K(x,y)=a(x,y)/|y|^{n+\sigma}$ $(\sigma\in(0,2))$ in a bounded domain by a geometric method, where functions $a(.,y)$ are uniformly bounded and equicontinuous on the variable $y$. Our results generalize the classical Calderon-Zgymund estimates. The analytical tools used in this paper are Hardy-Littlewood maximum functions, energy estimates and Besicovich’s covering lemma. The main difficulty in proving these results is that the kernels are non-local.
