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

preprint2022arXivOpen access

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

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

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