Regularity results for a class of quasiconvex functionals with nonstandard growth

• Emilio Acerbi ^[1] ; Giuseppe Mingione ^[1]
  1. [1] Università di Parma, Italia
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 30, Nº 2, 2001, págs. 311-339
• Idioma: inglés
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• Resumen

  • We consider the integral ftinctional f f (x, Du) dx under non standard growth assumptions of (p, q)-type: namely, we assume that for some function p(x) > 1, a condition appearing in several models from mathematical physics. Under sharp assumptions on the continuous function p (x ) we prove partial regularity of minimizers in the vector-valued case u : R" -~ allowing for quasiconvex energy densities. This is, to our knowledge, the first regularity theorem for quasiconvex functionals under non standard growth conditions