Curvature estimation of the level sets of solutions of a class of elliptic partial differential equation

Xuemei Yu

doi:10.1117/12.2679047

14 June 2023 Curvature estimation of the level sets of solutions of a class of elliptic partial differential equation

Xuemei Yu

Proceedings Volume 12725, International Conference on Pure, Applied, and Computational Mathematics (PACM 2023); 1272507 (2023) https://doi.org/10.1117/12.2679047
Event: International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), 2023, Suzhou, China

Abstract

The curvature of the level set of elliptic partial differential equation solutions is always an important content in the study of convexity. Curvature is an important invariant of surface, which characterizes the degree of curve bending, is the important basis of differential geometry. Curvature is widely used in machining. In this paper, we study the completely nonlinear elliptic Monge-Ampère equation det D²u = e^u with 0 boundary value Dirichlet condition in four-dimensional Euclidean space. It is proved that the auxiliary function obtains the maximum value at the boundary, and then the mean curvature and Gauss curvature of the level sets of the solutions of the equation are estimated quantitatively.

Citation Download Citation

Xuemei Yu "Curvature estimation of the level sets of solutions of a class of elliptic partial differential equation", Proc. SPIE 12725, International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), 1272507 (14 June 2023); https://doi.org/10.1117/12.2679047

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