Abstract
Abstract For solutions of capillarity problems with the boundary contact angle being bounded away from 0 and π and the mean curvature being bounded from above and below, we show the Lipschitz continuity of a solution up to the boundary locally in any neighborhood in which the solution is bounded and ∂Ω is 𝐶2; the Lipschitz norm is determined completely by the upper bound of | cos θ|, together with the lower and upper bounds of 𝐻, the upper bound of the absolute value of the principal curvatures of ∂Ω and the dimension 𝑛.
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