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EPSRC Reference: EP/W006898/1
Title: Generalised Hörmander-Rellich-Pohozhaev-Morawetz identities and their applications in spectral geometry
Principal Investigator: Levitin, Professor M
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics and Statistics
Organisation: University of Reading
Scheme: Standard Research - NR1
Starts: 01 June 2022 Ends: 31 May 2023 Value (£): 49,555
EPSRC Research Topic Classifications:
Algebra & Geometry Mathematical Analysis
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
26 May 2021 EPSRC Mathematical Sciences Small Grants Panel May 2021 Announced
Summary on Grant Application Form
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.
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Organisation Website: http://www.rdg.ac.uk