Calderón-Zygmund estimates for quasilinear elliptic double obstacle problems with variable exponent and logarithmic growth

Abstract

Quasilinear elliptic double obstacle problems with variable exponent and logarithmic growth are studied. We obtain a global Calderon-Zygmund estimate for such an irregular obstacle problem by proving that the gradient of the solution is as integrable as both the nonhomogeneous term and the gradient of the associated double obstacles under minimal regularity requirements on the elliptic operator over the boundary of the nonsmooth domain.