Regularity Results for a Class of Obstacle Problems under Non Standard Growth Conditions

We prove regularity results for minimizers of functionals F(u, Ω) := Ω f(x, u, Du) dx in the class K := {u ∈ W 1,p(x)(Ω,R) : u ≥ ψ}, where ψ : Ω → R is a fixed function and f is quasiconvex and fulfills a growth condition of the type L−1|z|p(x) ≤ f(x, ξ, z) ≤ L(1 + |z|p(x)), with growth exponent p : Ω → (1,∞).