Morrey regularity and continuity results for almost minimizers of asymptotically convex integrals

Mikil Foss ¹   ; Antonia Passarelli di Napoli ²   ; Anna Verde ²

¹ Department of Mathematics University of Nebraska-Lincoln 203 Avery Hall Lincoln, NE 68588-0130, U.S.A.
² Dipartimento di Matematica “R. Caccioppoli” Università di Napoli “Federico II” Via Cintia 80126 Napoli, Italy

Applicationes Mathematicae, Tome 35 (2008) no. 3, pp. 335-353

Résumé

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.

Détail

DOI : 10.4064/am35-3-6

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