Upper Bound of Critical Sets of Solutions of Elliptic Equations in the Plane
Document Type
Article
Publication Date
10-1-2023
Abstract
In this note, we investigate the measure of singular sets and critical sets of real-valued solutions of elliptic equations in two dimensions. These singular sets and critical sets are finitely many points in the plane. Adapting the Carleman estimates involving polynomial functions at singularities by Donnelly and Fefferman (J. Amer. Math. Soc. 3, 333–353, 1990), we obtain the upper bounds of singular points and critical points.
Publication Source (Journal or Book title)
Vietnam Journal of Mathematics
First Page
799
Last Page
810
Recommended Citation
Zhu, J. (2023). Upper Bound of Critical Sets of Solutions of Elliptic Equations in the Plane. Vietnam Journal of Mathematics, 51 (4), 799-810. https://doi.org/10.1007/s10013-023-00614-6