Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle

0575046 - ÚJF 2024 RIV US eng J - Článek v odborném periodiku
Krejčiřík, D. - Lotoreichik, Vladimir - Vu, T.
Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle.
Applied Mathematics and Optimization. Roč. 88, č. 2 (2023), č. článku 63. ISSN 0095-4616. E-ISSN 1432-0606
Grant CEP: GA ČR(CZ) GA21-07129S
Institucionální podpora: RVO:61389005
Klíčová slova: Robin Laplacian * Lowest eigenvalue * Spectral optimisation * Triangles
Obor OECD: Applied mathematics
Impakt faktor: 1.8, rok: 2022
Způsob publikování: Open access
https://doi.org/10.1007/s00245-023-10033-1

We consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. We prove that the equilateral triangle is a local maximiser of the lowest eigenvalue among all triangles of a given area provided that the negative boundary parameter is sufficiently small in absolute value, with the smallness depending on the area only. Moreover, using various trial functions, we obtain sufficient conditions for the global optimality of the equilateral triangle under fixed area constraint in the regimes of small and large couplings. We also discuss the constraint of fixed perimeter.
Trvalý link: https://hdl.handle.net/11104/0344892