Calculus of Variations and Geometric Measure Theory
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G. Mingione

Bounds for the singular set of solutions to non linear elliptic systems

created on 02 Dec 2002
modified by mingione on 30 Sep 2012

[BibTeX]

Published Paper

Inserted: 2 dec 2002
Last Updated: 30 sep 2012

Journal: Calc. Var.
Volume: 18
Number: 4
Pages: 373-400
Year: 2003
Notes:

Preprint no.43, SFB 611, University of Bonn


Abstract:

We give new estimates for the Hausdorff dimension of the singular set of solutions to elliptic systems: $$ - \mbox { div } a(x,u,Du) = b(x,u,Du)\;.$$ \noindent If the vector fields $a$ and $b$ are Hölder continuous with respect to the variables $(x,u)$ with exponent $\alpha$, then, under suitable assumptions, the Hausdorff dimension of the singular set of any weak solution is at most $n-2\alpha$. We consider natural growth assumptions on $a(x,u,Du)$ with respect to $u$ and critical ones on the right hand side $b(x,u,Du)$ with respect to $Du$.

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