Construction of Twice Differentiable Functions with Continuous Laplacian and Bounded Hessian

Published 18 Oct 2022 in math.AP and math.CV | (2210.10099v2)

Abstract: We construct examples of twice differentiable functions in $\mathbb{R}^n$ with continuous Laplacian and bounded Hessian. The same construction is also applicable to higher order differentiability, the Monge-Amp`ere equation, and mean curvature equation for hypersurfaces.

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