The Boundary Harnack Principle for Nonlocal Elliptic Operators in Non-divergence Form

被引：12

作者：

Ros-Oton, Xavier ^{[1
]}

Serra, Joaquim ^{[2
]}

机构：

[1] Univ Texas Austin, Dept Math, 2515 Speedway, Austin, TX 78751 USA

[2] Swiss Fed Inst Technol, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

来源：

POTENTIAL ANALYSIS | 2019年 / 51卷 / 03期

关键词：

Integro-differential elliptic equations; Boundary Harnack; REGULARITY;

D O I：

10.1007/s11118-018-9713-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a boundary Harnack inequality for nonlocal elliptic operators L in non-divergence form with bounded measurable coefficients. Namely, our main result establishes that if Lu-1 = Lu-2 = 0 in omega boolean AND B-1, u(1) = u(2) = 0 in B-1 set minus omega, and u(1),u(2) >= 0 in Double-struck capital R-n, then u(1) and u(2) are comparable in B-1/2. The result applies to arbitrary open sets omega. When omega is Lipschitz, we show that the quotient u(1)/u(2) is Holder continuous up to the boundary in B-1/2. These results will be used in forthcoming works on obstacle-type problems for nonlocal operators.

引用

页码：315 / 331

页数：17

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