## F. Duzaar - A. Gastel - G. Mingione

# Elliptic systems, singular sets and Dini continuity

created on 02 Nov 2003

modified on 19 Oct 2004

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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 HÃ¶lder 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.