Examples of Twice Differentiable Functions with Continuous Laplacian and Bounded Discontinuous Hessian
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.
Authors
- Yu Yan (ORCID: https://orcid.org/0000-0002-3528-5320)
- Yifei Pan null
Publication Details
- Journal
- Analysis in Theory and Applications
- Published
- 2024-10-17
- DOI
- https://doi.org/10.4208/ata.oa-2024-0017
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 0.00