Asymptotically regular problems I: Higher integrability - Scheven, Christoph; Schmidt, Thomas (Journal of Differential Equations, 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. © 2009 Elsevier Inc. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2010.nat.dma.lma2.asympt
Keywords: Calculus of variations; Calderon-Zygmund estimates; Higher integrability; Minimizing sequence; Quasilinear elliptic system