Upper bound of critical sets of solutions of elliptic equations in the plane
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 in DF90, we obtain the upper bounds of singular points and critical points.
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