arrow
Volume 40, Issue 3
Examples of Twice Differentiable Functions with Continuous Laplacian and Bounded Discontinuous Hessian

Yifei Pan & Yu Yan

Anal. Theory Appl., 40 (2024), pp. 311-334.

Published online: 2024-10

Export citation
  • 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.

  • AMS Subject Headings

35Axx

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@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.

Pan , Yifei and Yan , Yu. (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
Copy to clipboard
The citation has been copied to your clipboard