Abstract and Applied Analysis
Volume 2004 (2004), Issue 1, Pages 27-44
doi:10.1155/S1085337504310079
Regularity of minimizers for nonconvex vectorial integrals with
p-q growth via relaxation methods
Dipartimento di Matematica “Ulisse Dini”, Università di Firenze, Viale Morgagni 67/A, Firenze 50134, Italy
Received 10 January 2003
Copyright © 2004 Irene Benedetti and Elvira Mascolo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Local Lipschitz continuity of local minimizers of vectorial integrals ∫Ω f(x,Du)dx is proved when f satisfies p-q growth condition and ξ↦f(x,ξ) is not convex. The uniform convexity and the radial structure condition with respect to the last variable are assumed only at infinity. In the proof, we use semicontinuity and relaxation results for functionals with nonstandard growth.