Regularity of minimizers of autonomous convex variational integrals

• Menita Carozza ^[2] ; Jan Kristensen ^[1] ; Antonia Passarelli di Napoli ^[3]
  1. [1] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
  2. [2] Università del Sannio, Italia
  3. [3] Università di Napoli Federico II, Italia

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 13, Nº 4, 2014, págs. 1065-1089
• Idioma: inglés
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• Resumen

  • We establish local higher integrability and differentiability results for minimizers of variational integrals F(v,) = Z  F(Dv(x)) dx overW1,p-Sobolev mappings v :  ⇢ Rn !RN satisfying a Dirichlet boundary condition. The integrands F are assumed to be autonomous, convex and of (p, q) growth, but are otherwise not subjected to any further structure conditions, and we consider exponents in the range 1 < p  q < p⇤, where p⇤ denotes the Sobolev conjugate exponent of p.