Global L∞-estimates and Hölder continuity of weak solutions to elliptic equations with the general nonstandard growth conditions

We study the elliptic equations in divergence form with the general nonstandard growth conditions involving Lebesgue measurable functions on Ω. In this paper we prove global L∞-estimates and Hölder continuity of weak solutions for these equations. Our results improve the one in Giusti (2003) even for the case when p(x)≡p and q(x)≡q are constants.