Calculus of Variations and Geometric Measure Theory
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F. Duzaar - A. Gastel - G. Mingione

Elliptic systems, singular sets and Dini continuity

created on 02 Nov 2003
modified on 19 Oct 2004

[BibTeX]

Published Paper

Inserted: 2 nov 2003
Last Updated: 19 oct 2004

Journal: Comm. Partial Differential Equations
Volume: 29
Number: 7&8
Pages: 1215-1240
Year: 2004

Abstract:

We estimate the singular set of solutions to elliptic systems with linear growth of the type $$-div a(x,u,Du) = b(x,u,Du)\;,$$ where $a(x,u,Du)$ depends in a Dini continuous way on $(x,u)$; this is the natural limit case of Hölder continuity of the coefficients for proving partial continuity of the gradient, as shown by Duzaar & Gastel (Archiv der Mathematik, 2002). The singular set is estimated using Hausdorff measures generated by functions which are not powers.

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