Calculus of Variations and Geometric Measure Theory
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L. Beck

Partial Hölder continuity for solutions of subquadratic elliptic systems in low dimensions

created by beck on 11 Nov 2009
modified on 10 Jan 2013


Published Paper

Inserted: 11 nov 2009
Last Updated: 10 jan 2013

Journal: J. Math. Anal. Appl.
Volume: 354
Number: 1
Pages: 301-318
Year: 2009
Doi: 10.1016/j.jmaa.2008.12.042


We consider weak solutions of second order nonlinear elliptic systems in divergence form under standard subquadratic growth conditions with boundary data of class $C^1$. In dimensions $n \in \{2,3\}$ we prove that $u$ is locally Hölder continuous for every exponent $\lambda \in (0,1-\frac{n-2}{p})$ outside a singular set of Hausdorff dimension less than $n-p$. This result holds up to the boundary both for non-degenerate and degenerate systems. In the proof we apply the direct method and classical Morrey-type estimates introduced by Campanato.


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