Guidorzi M.: Existence and regularity of minimizers of nonconvex integrals with p - q growth

Abstract. We show that local minimizers of functionals of the form∫ Ω [f(Du(x)) + g(x, u(x))] dx, u ∈ u0 +W 1,p0 (Ω), are locally Lipschitz continuous provided f is a convex function with p−q 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. Mathematics Subject Classification. 49N60, 49J10. Received July 7, 2005