Continuity Points Via Riesz Potentials for ℂ-Elliptic Operators-Reference-Cited by-同舟云学术

Continuity Points Via Riesz Potentials for ℂ-Elliptic Operators

Published:2020-09-19 Issue:4 Volume:71 Page:1201-1218
ISSN:0033-5606
Container-title:The Quarterly Journal of Mathematics
language:en
Short-container-title:

Author:

Diening Lars¹,Gmeineder Franz²

Affiliation:

1. Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany

2. Mathematical Institute, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany

Abstract

Abstract We establish a Riesz potential criterion for Lebesgue continuity points of functions of bounded $\mathbb{A}$-variation, where $\mathbb{A}$ is a $\mathbb{C}$-elliptic differential operator of arbitrary order. This result generalizes a potential criterion that is known for full gradients to the case where full gradient estimates are not available by virtue of Ornstein’s non-inequality.

Funder

DFG

Hausdorff Centre for Mathematics, Bonn, and the University of Bielefeld

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/qjmath/article-pdf/71/4/1201/35093135/haaa027.pdf

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