A characterization of capillary spherical caps by a partially overdetermined problem in a half ball
Xiaohan Jia, Zheng Lu, Chao Xia, Xuwen Zhang
TL;DR
This paper proves a rigidity result characterizing capillary spherical caps in a half ball through a Serrin-type overdetermined boundary value problem, extending understanding of capillary surfaces in geometric analysis.
Contribution
It introduces a new characterization of capillary spherical caps using a partially overdetermined problem in a half ball, providing a novel rigidity result.
Findings
Characterization of capillary spherical caps
Rigidity result for a Serrin-type problem
Extension of geometric analysis of capillary surfaces
Abstract
In this note, we study a Serrin-type partially overdetermined problem proposed by Guo-Xia (Calc. Var. Partial Differential Equations 58: no. 160, 2019. https://doi.org/10.1007/s00526-019-1603-3, and prove a rigidity result that characterizes capillary spherical caps in a half ball.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Contact Mechanics and Variational Inequalities · Advanced Mathematical Modeling in Engineering