Work

Examples of Twice Differentiable Functions with Continuous Laplacian and Bounded Discontinuous Hessian

Year: 2024

Type: article

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.

Source: Analysis in Theory and Applications

DOI: 10.4208/ata.oa-2024-0017

Authors: Yifei Pan, Yu Yan

Institutions: Purdue University Fort Wayne, Biola University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4403496024

FWCI:

Cites: 5

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Related to: 10