Morrey regularity and continuity results for almost minimizers of asymptotically convex integrals
Tom 35 / 2008
Applicationes Mathematicae 35 (2008), 335-353
MSC: 49N60, 35B65.
DOI: 10.4064/am35-3-6
Streszczenie
In a recent paper [Forum Math., 2008] the authors established some global, up to the boundary of a domain $\mit\Omega\subset{\mathbb R}^n$, continuity and Morrey regularity results for almost minimizers of functionals of the form $\mathbf u\mapsto\int_{\mit\Omega}g(\mathbf x,\mathbf u(\mathbf x), %{\mathbf \nabla}% \nabla \mathbf u(\mathbf x))\,d\mathbf x$. The main assumptions for these results are that $g$ is asymptotically convex and that it satisfies some growth conditions. In this article, we present a specialized but significant version of this general result. The primary purpose of this paper is provide several applications of this simplified result.
