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arXiv · 2210.10099

Construction of Twice Differentiable Functions with Continuous Laplacian and Bounded Hessian

Yifei Pan·Yu Yan
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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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Yifei Pan, Yu Yan. 2022-10-18. Construction of Twice Differentiable Functions with Continuous Laplacian and Bounded Hessian. https://arxiv.org/abs/2210.10099

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