A general regularity theorem for functionals with phi-growth

Dominic Breit, Bianca Stroffolini, Anna Verde

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14 Citations (Scopus)

Abstract

We prove C(1,alpha)-regularity for local minimizers of functionals

integral(Omega)phi vertical bar del u vertical bar)dx,

where phi is a Young function. In order to generalize the results of Fuchs (2011) [9] and Diening et al. (2009) [6], we assume for the function phi only the (Delta 2)-condition and phi ''(t) >= (epsilon) over cap phi'(t)/t for a positive constant (epsilon) over cap (and derivatives). of course a Holder-condition for the second (C) 2011 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)226-233
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Volume383
Issue number1
DOIs
Publication statusPublished - Nov 2011

Keywords

  • Vector-valued problems
  • Local minimizers
  • Nonstandard growth
  • Regularity
  • NONLINEAR ELLIPTIC-SYSTEMS
  • VARIATIONAL INTEGRALS
  • MINIMIZERS

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