Splitting-type variational problems with x-dependent exponents

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this article we prove regularity results for locally bounded minimizers u: R(n) superset of Omega -> R(N) of functionals of the type

integral(Omega) [(1 + vertical bar del(1)u vertical bar(2))(P(x)/2) + (1 + vertical bar del(2)u vertical bar(2))(q(x)/2)] dx,

where p and q are Lipschitz-functions and del u = (del(1)u, del(2)u) is an arbitrary decompositon of the gradient of u. Related functionals are the topic of the paper [IBr3], but the situation here is not covered.

Original languageEnglish
Pages (from-to)279-289
Number of pages11
JournalAnnales Academiæ Scientiarum Fennicæ. Mathematica
Volume36
Issue number1
DOIs
Publication statusPublished - 2011

Keywords

  • Variational problems of splitting-type
  • regularity of minimizers
  • nonautonomous functionals
  • GROWTH-CONDITIONS
  • HIGHER INTEGRABILITY
  • REGULARITY
  • INTEGRALS
  • MINIMIZERS
  • GRADIENT

Cite this