Besov Regularity Estimates for a Class of Obstacle Problems with Variable Exponents

In this paper we obtain the local regularity estimates in Besov spaces of weak solutions for a class of elliptic obstacle problems with variable exponents p(x). We deal with the case in which the solutions to the obstacle problems satisfy a variational inequality in the following form integral(Omega)< A(x,Du), D(phi-u)> dx >=integral(Omega)< F, D(phi-u)> dx under some proper assumptions on the function p(x), A, phi and F. Moreover, we would like to point out that our results improve the known results for such problems.