Examples of Twice Differentiable Functions in $\mathbb{R}^n$ with Continuous Laplacian and Unbounded Hessian

Yifei Pan; Yu Yan

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arXiv · 2208.13123

Examples of Twice Differentiable Functions in $\mathbb{R}^n$ with Continuous Laplacian and Unbounded 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 unbounded Hessian. The same construction is also applicable to higher order differentiability.

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Yifei Pan, Yu Yan. 2022-08-28. Examples of Twice Differentiable Functions in $\mathbb{R}^n$ with Continuous Laplacian and Unbounded Hessian. https://arxiv.org/abs/2208.13123

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