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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Serrin-type theorems for triangles
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by Ilaria Fragalà and Bozhidar Velichkov PDF
Proc. Amer. Math. Soc. 147 (2019), 1615-1626 Request permission


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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Additional Information
  • Ilaria Fragalà
  • Affiliation: Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy
  • MR Author ID: 629098
  • Email:
  • Bozhidar Velichkov
  • Affiliation: Laboratoire Jean Kuntzmann (LJK), Université Grenoble Alpes, Bâtiment IMAG, 700 Avenue Centrale, 38401 Saint-Martin-d’Hères, France
  • MR Author ID: 1000813
  • Email:
  • Received by editor(s): May 14, 2018
  • Received by editor(s) in revised form: August 9, 2018
  • Published electronically: January 8, 2019
  • Additional Notes: The authors have been supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).
    The second author has been partially supported by ANR through the projects GeoSpec (LabEx PERSYVAL-Lab, ANR-11- LABX-0025-01) and CoMeDiC (ANR-15-CE40-0006).
  • Communicated by: Joachim Krieger
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 1615-1626
  • MSC (2010): Primary 35N25, 35J57, 49Q10
  • DOI:
  • MathSciNet review: 3910426