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Type: Journal article
Title: Realisations of elliptic operators on compact manifolds with boundary
Author: Bandara, L.
Goffeng, M.
Saratchandran, H.
Citation: Advances in Mathematics, 2023; 420:108968-108968
Publisher: Elsevier BV
Issue Date: 2023
ISSN: 0001-8708
Statement of
Lashi Bandara, Magnus Goffeng, Hemanth Saratchandran
Abstract: This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of Bär-Ballmann to first order elliptic operators. The space of possible boundary values of elements in the maximal domain is described as a Hilbert space densely sandwiched between two mixed order Sobolev spaces. The description uses Calderón projectors which, in the first order case, is equivalent to results of Bär-Bandara using spectral projectors of an adapted boundary operator. Boundary conditions that induce Fredholm as well as regular realisations, and those that admit higher order regularity, are characterised. In addition, results concerning spectral theory, homotopy invariance of the Fredholm index, and well-posedness for higher order elliptic boundary value problems are proven.
Keywords: Elliptic differential operator; Fredholm boundary conditions; Boundary regularity; Calderón projector
Rights: © 2023 Published by Elsevier Inc.
DOI: 10.1016/j.aim.2023.108968
Appears in Collections:Australian Institute for Machine Learning publications

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