
Journal of Convex Analysis 22 (2015), No. 1, 219246 Copyright Heldermann Verlag 2015 Partial Hölder Continuity of Minimizers of Functionals Satisfying a General Asymptotic Relatedness Condition Mikil Foss Dept. of Mathematics, University of Nebraska, Lincoln, NE 68588, U.S.A. mfoss2@math.unl.edu Christopher S. Goodrich Dept. of Mathematics, Creighton Preparatory School, Omaha, NE 68114, U.S.A. and: Dept. of Mathematics, University of Rhode Island, Kingston, RI 02881, U.S.A. cgood@prep.creighton.edu [Abstractpdf] We consider the partial H\"{o}lder continuity of minimizers of functionals of the form $$v\mapsto\int_{\Omega}f(x,v,Dv)\ dx,$$ where $\Omega\subseteq\mathbb{R}^n$ is open and bounded. In our setting the integrand $f\ : \ \Omega\times\mathbb{R}^N\times \mathbb{R}^{N\times n}\rightarrow\mathbb{R}$ is not necessarily continuous in any of its three arguments. In particular, due to the use of a suitable asymptotic relatedness condition, $f$ possesses continuity and convexity only as the norm of its third argument tends to infinity. Since, in particular, $v$ is possibly vectorvalued, this provides a generalization of certain existing regularity results in the literature and helps to further build a loworder regularity theory. Keywords: Partial regularity, Morrey regularity, Hoelder continuity. MSC: 49N60; 46E35 [ Fulltextpdf (217 KB)] for subscribers only. 