Abstract and Applied Analysis
Volume 2004 (2004), Issue 1, Pages 27-44

Regularity of minimizers for nonconvex vectorial integrals with p-q growth via relaxation methods

Irene Benedetti and Elvira Mascolo

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.


Local Lipschitz continuity of local minimizers of vectorial integrals Ωf(x,Du)dx is proved when f satisfies p-q growth condition and ξf(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.