Abstract
In this paper we show that a solution of the equation − Δ p ( x ) u = μ is Hölder continuous with exponent α if and only if the nonnegative Radon measure μ satisfies the growth condition μ ( B r ( x ) ) ≤ C r n − p ( x ) + α ( p ( x ) − 1 ) for any ball B r ( x ) ⊂ Ω , with r 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 p -Laplace operator with p constant.
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