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

Volume 35 / 2008

Mikil Foss, Antonia Passarelli di Napoli, Anna Verde Applicationes Mathematicae 35 (2008), 335-353 MSC: 49N60, 35B65. DOI: 10.4064/am35-3-6

Abstract

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.

Authors

  • Mikil FossDepartment of Mathematics
    University of Nebraska-Lincoln
    203 Avery Hall
    Lincoln, NE 68588-0130, U.S.A.
    e-mail
  • Antonia Passarelli di NapoliDipartimento di Matematica “R. Caccioppoli”
    Università di Napoli “Federico II”
    Via Cintia
    80126 Napoli, Italy
    e-mail
  • Anna VerdeDipartimento di Matematica “R. Caccioppoli”
    Università di Napoli “Federico II”
    Via Cintia
    80126 Napoli, Italy
    e-mail

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