Generalised Hörmander-Rellich-Pohozhaev-Morawetz identities and their applications in spectral geometry
Lead Research Organisation:
University of Reading
Department Name: Mathematics and Statistics
Abstract
Spectral theory studies the mathematical models usually arising in wave motion, either in continuum mechanics or in quantum physics, and the abstract analogues. Most of the problems involving partial differential equations cannot be solved analytically. Spectral geometry studies the links between the underlying geometry and the spectral properties of operators, both direct and inverse.
We propose to investigate some long stranding conjectures in spectral geometry, and some new problems, using the method of multipliers commonly associated with the names of Hörmander, Rellich, Pohozhaev and Morawetz. This method leads to identities which are a priori satisfied by eigenfunctions of a boundary value problem, and which can be used to extract the relevant geometric information.
We propose to investigate some long stranding conjectures in spectral geometry, and some new problems, using the method of multipliers commonly associated with the names of Hörmander, Rellich, Pohozhaev and Morawetz. This method leads to identities which are a priori satisfied by eigenfunctions of a boundary value problem, and which can be used to extract the relevant geometric information.
Organisations
Publications
Capoferri M
(2023)
Two-Term Spectral Asymptotics in Linear Elasticity
in The Journal of Geometric Analysis
Capoferri M
(2022)
Two-term spectral asymptotics in linear elasticity
Filonov N
(2023)
Pólya's conjecture for Euclidean balls
in Inventiones mathematicae
Filonov N
(2022)
Pólya's conjecture for Euclidean balls