Calculus of Variations and Geometric Measure Theory
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C. Scheven - T. Schmidt

Asymptotically regular problems I: Higher integrability

created by schmidt on 22 Feb 2012
modified on 07 Mar 2012


Published Paper

Inserted: 22 feb 2012
Last Updated: 7 mar 2012

Journal: J. Differ. Equations
Volume: 248
Number: 4
Pages: 745-791
Year: 2010
Links: Link to the published version


We consider weak solutions $u$ of non-linear systems of partial differential equations. Assuming that the system exhibits a certain kind of elliptic behavior near infinity we prove higher integrability results for the gradient $Du$. In particular, we establish Hölder continuity of $u$ in low dimensions. Moreover, we obtain analogous results for vectorial minimizers of multi-dimensional variational integrals. Finally, we discuss an extension to minimizing sequences and applications to generalized minimizers.


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