Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones

0566027 - ÚJF 2023 RIV DE eng J - Článek v odborném periodiku
Khalile, M. - Lotoreichik, Vladimir
Spectral isoperimetric inequalities for Robin Laplacians on 2-manifolds and unbounded cones.
Journal of Spectral Theory. Roč. 12, č. 2 (2022), s. 683-706. ISSN 1664-039X. E-ISSN 1664-0403
Grant CEP: GA ČR GA17-01706S
Institucionální podpora: RVO:61389005
Klíčová slova: Robin Laplacian * 2-manifold * unbounded conical domain * lowest eigenvalue * spectral isoperimetric inequality * parallel coordinates
Obor OECD: Pure mathematics
Impakt faktor: 1, rok: 2022
Způsob publikování: Open access
https://doi.org/10.4171/JST/416

We consider the problem of geometric optimization of the lowest eigenvalue for the Laplacian on a compact, simply-connected two-dimensional manifold with boundary subject to an attractive Robin boundary condition. We prove that in the sub-class of manifolds with the Gauss curvature bounded from above by a constant K-o >= 0 and under the constraint of fixed perimeter, the geodesic disk of constant curvature K-o maximizes the lowest Robin eigenvalue. In the same geometric setting, it is proved that the spectral isoperimetric inequality holds for the lowest eigenvalue of the Dirichlet-to-Neumann operator. Finally, we adapt our methods to Robin Laplacians acting on unbounded three-dimensional cones to show that, under a constraint of fixed perimeter of the cross-section, the lowest Robin eigenvalue is maximized by the circular cone.
Trvalý link: https://hdl.handle.net/11104/0337466