Examples of twice differentiable functions with continuous Laplacian and unbounded Hessian

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

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Bibliographic Details
Published in:Collectanea mathematica (Barcelona) 2024-05, Vol.75 (2), p.453-479
Main Authors: Pan, Yifei, Yan, Yu
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Continuity (mathematics)
Geometry
Mathematics
Mathematics and Statistics
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Description
Summary:We construct examples of twice differentiable functions in R n with continuous Laplacian and unbounded Hessian. The same construction is also applicable to higher order differentiability.
ISSN:0010-0757
2038-4815
DOI:10.1007/s13348-023-00395-8