Hölder continuity of image-superharmonic functions Original Research Article

In this paper we show that a solution of the equation −Δp(x)u=μ−Δp(x)u=μ is Hölder continuous with exponent αα if and only if the nonnegative Radon measure μμ satisfies the growth condition μ(Br(x))≤Crn−p(x)+α(p(x)−1)μ(Br(x))≤Crn−p(x)+α(p(x)−1) for any ball View the MathML sourceBr(x)⊂Ω, with rr small enough. This extends an old result of Lewy and Stampacchia for the Laplace operator, and a recent result of Kilpeläinen and Zhong for the pp-Laplace operator with pp constant.