# Asymptotically regular problems I: Higher integrability

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

[BibTeX]

Published Paper

Inserted: 22 feb 2012
Last Updated: 7 mar 2012

Journal: J. Differ. Equations
Volume: 248
Number: 4
Pages: 745-791
Year: 2010
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.