Regularity for non-autonomous functionals with almost linear growth

Dominic Breit, Bruno De Maria, Antonia Passarelli di Napoli

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We consider non-autonomous functionals F (u; Omega) = integral(Omega) f(x, Du) dx, where the density f : Omega x R(nN) -> R has almost linear growth, i.e., f(x, xi) approximate to vertical bar xi vertical bar log (1 + vertical bar xi vertical bar). We prove partial C (1,gamma) -regularity for minimizers u: R(n) superset of Omega -> R(N) under the assumption that D (xi) f (x, xi) is Holder continuous with respect to the x-variable. If the x-dependence is C (1) we can improve this to full regularity provided additional structure conditions are satisfied.

Original languageEnglish
Pages (from-to)83-114
Number of pages32
JournalManuscripta Mathematica
Volume136
Issue number1-2
DOIs
Publication statusPublished - Sep 2011

Keywords

  • VARIATIONAL INTEGRALS
  • CASE 1-LESS-THAN-P-LESS-THAN-2
  • CONVEX INTEGRALS
  • SINGULAR SET
  • MINIMIZERS

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