Examples of Twice Differentiable Functions in ℝⁿ with Continuous Laplacian and Unbounded Hessian

2022/08/28 by Yifei Pan, Yu Yan, Pan, Yifei +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2208.13123

openalex publication_date 2022/08/28 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

Abstract

We construct examples of twice differentiable functions in ℝⁿ with continuous Laplacian and unbounded Hessian. The same construction is also applicable to higher order differentiability.

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