Higher differentiability of solutions for a class of obstacle problems with variable exponents

In this paper we prove a higher differentiability result for the solutions to class of obstacle problems in formmin⁡{∫ΩF(x,Dw)dx:w∈Kψ(Ω)} where ψ∈W1,p(x)(Ω) is fixed function called and Kψ(Ω)={w∈W01,p(x)(Ω)+u0:w≥ψa.e. Ω} admissible functions, suitable boundary value u0. We deal with convex integrand F which satisfies p(x)-growth conditions|ξ|p(x)≤F(x,ξ)≤C(1+|ξ|p(x)),p(x)>1.