Header

UZH-Logo

Maintenance Infos

The boundary Harnack principle for nonlocal elliptic operators in non-divergence form


Ros-Oton, Xavier; Serra, Joaquim (2019). The boundary Harnack principle for nonlocal elliptic operators in non-divergence form. Potential Analysis, 51(3):315-331.

Abstract

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 Lu1 = Lu2 = 0 in Ω ∩ B1, u1 = u2 = 0 in B1 ∖Ω, and u1,u2 ≥ 0 in ℝn, then u1 and u2 are comparable in B1/2. The result applies to arbitrary open sets Ω. When Ω is Lipschitz, we show that the quotient u1/u2 is Hölder continuous up to the boundary in B1/2. These results will be used in forthcoming works on obstacle-type problems for nonlocal operators.

Abstract

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 Lu1 = Lu2 = 0 in Ω ∩ B1, u1 = u2 = 0 in B1 ∖Ω, and u1,u2 ≥ 0 in ℝn, then u1 and u2 are comparable in B1/2. The result applies to arbitrary open sets Ω. When Ω is Lipschitz, we show that the quotient u1/u2 is Hölder continuous up to the boundary in B1/2. These results will be used in forthcoming works on obstacle-type problems for nonlocal operators.

Statistics

Citations

Dimensions.ai Metrics
1 citation in Web of Science®
2 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

11 downloads since deposited on 09 Jan 2020
5 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Uncontrolled Keywords:Analysis
Language:English
Date:1 October 2019
Deposited On:09 Jan 2020 12:31
Last Modified:29 Jul 2020 12:59
Publisher:Springer
ISSN:0926-2601
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s11118-018-9713-7

Download

Green Open Access

Download PDF  'The boundary Harnack principle for nonlocal elliptic operators in non-divergence form'.
Preview
Content: Submitted Version
Language: English
Filetype: PDF
Size: 224kB