Global L∞-estimates and Hölder continuity of weak solutions to elliptic equations with the general nonstandard growth conditions. (June 2017) - Yu, Cholhun
Abstract: 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.