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

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