Examples of Twice Differentiable Functions with Continuous Laplacian and Bounded Discontinuous Hessian
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@Article{ATA-40-311,
author = {Pan , Yifei and Yan , Yu},
title = {Examples of Twice Differentiable Functions with Continuous Laplacian and Bounded Discontinuous Hessian},
journal = {Analysis in Theory and Applications},
year = {2024},
volume = {40},
number = {3},
pages = {311--334},
abstract = {
We construct examples of twice differentiable functions in $\mathbb{R}^n$ with continuous Laplacian and bounded discontinuous Hessian. The same construction is also applicable to higher order differentiability, the Monge-Ampère equation, and the mean curvature equation for hypersurfaces.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2024-0017}, url = {http://global-sci.org/intro/article_detail/ata/23468.html} }
TY - JOUR
T1 - Examples of Twice Differentiable Functions with Continuous Laplacian and Bounded Discontinuous Hessian
AU - Pan , Yifei
AU - Yan , Yu
JO - Analysis in Theory and Applications
VL - 3
SP - 311
EP - 334
PY - 2024
DA - 2024/10
SN - 40
DO - http://doi.org/10.4208/ata.OA-2024-0017
UR - https://global-sci.org/intro/article_detail/ata/23468.html
KW - Twice differentiable, continuous Laplacian, bounded Hessian.
AB -
We construct examples of twice differentiable functions in $\mathbb{R}^n$ with continuous Laplacian and bounded discontinuous Hessian. The same construction is also applicable to higher order differentiability, the Monge-Ampère equation, and the mean curvature equation for hypersurfaces.
Yifei Pan & Yu Yan. (2024). Examples of Twice Differentiable Functions with Continuous Laplacian and Bounded Discontinuous Hessian.
Analysis in Theory and Applications. 40 (3).
311-334.
doi:10.4208/ata.OA-2024-0017
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