Calculus of Variations and Geometric Measure Theory

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

[BibTeX]

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

Abstract:

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.


Download: