Existence and regularity of minimizers of nonconvex integrals with p-q growth

¹ Dipartimento di Matematica – Università degli Studi di Parma, Parco Area delle Scienze 53/A, 43100 Parma, Italy; celada@math.unipr.it
² Dipartimento di Matematica “U. Dini” – Università degli Studi di Firenze, V. le Morgagni 67/A, 50134 Firenze Italy; cupini@math.unifi.it
³ Dipartimento di Matematica – Università degli Studi di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy; guidorzi@dm.unife.it

Received: 7 July 2005

Abstract

We show that local minimizers of functionals of the form ,  , are locally Lipschitz continuous provided f is a convex function with growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.