Regularity Results for Bounded Solutions to Obstacle Problems with Non-standard Growth Conditions

In this paper, we consider a class of obstacle problems of the typemin {integral(Omega) f(x, Dv) dx : v is an element of K-psi(Omega)}where psi is the obstacle, K-psi (Omega) = {v is an element of u(0)+W-0(1,p) (Omega, R) : v >= psi a.e. in Omega}, with v(0) is an element of W-1,W-p (Omega) a fixed boundary datum, the class of the admissible functions and the integrand f (x, Dv) satisfies non standard (p, q)-growth conditions. We prove higher differentiability results for bounded solutions of the obstacle problem under dimension-free conditions on the gap between the growth and the ellipticity exponents. Moreover, also the Sobolev assumption on the partial map x bar right arrow A(x, xi) is independent of the dimension n and this, in some cases, allows us to manage coefficients in a Sobolev class below the critical one W-1,W-n.