Upper bound of critical sets of solutions of elliptic equations in the plane

Jiuyi Zhu

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arXiv · 2112.10259

Upper bound of critical sets of solutions of elliptic equations in the plane

Jiuyi Zhu

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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 \cite{DF90}, we obtain the upper bounds of singular points and critical points.

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Jiuyi Zhu. 2021-12-19. Upper bound of critical sets of solutions of elliptic equations in the plane. https://arxiv.org/abs/2112.10259

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