Serrin-type theorems for triangles

Fragalà, Ilaria; Velichkov, Bozhidar

doi:10.1090/proc/14352

Serrin-type theorems for triangles
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by Ilaria Fragalà and Bozhidar Velichkov

Proc. Amer. Math. Soc. 147 (2019), 1615-1626

DOI: https://doi.org/10.1090/proc/14352

Published electronically: January 8, 2019

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Abstract:

We investigate interior and exterior overdetermined boundary value problems on triangles, which corresponds to studying stationary triangles for variational functionals under volume or perimeter constraint. We prove that in certain cases the only triangle supporting solution is the equilateral one. In some other cases, we obtain that all triangles support solutions, thus extending (through a simpler proof) what was recently shown by Hans Christianson [Proc. Amer. Math. Soc. 145 (2017), no. 12, 5247–5255].

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