Archive for Rational Mechanics and Analysis

, Volume 156, Issue 2, pp 121–140

Regularity Results for a Class of Functionals with Non-Standard Growth

  • Emilio Acerbi
  • Giuseppe Mingione

DOI: 10.1007/s002050100117

Cite this article as:
Acerbi, E. & Mingione, G. Arch. Rational Mech. Anal. (2001) 156: 121. doi:10.1007/s002050100117

Abstract:

We consider the integral functional
$$$$
under non-standard growth assumptions that we call p(x) type: namely, we assume that
$$$$
a relevant model case being the functional
$$$$
Under sharp assumptions on the continuous function p(x)>1 we prove regularity of minimizers. Energies exhibiting this growth appear in several models from mathematical physics.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Emilio Acerbi
    • 1
  • Giuseppe Mingione
    • 1
  1. 1.Dipartimento di Matematica¶Università di Parma¶Via D'Azeglio 85/A¶43100 Parma (Italy)¶E-mail: acerbi@prmat.math.unipr.it¶E-mail: mingione@prmat.math.unipr.itIT

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