Realisations of elliptic operators on compact manifolds with boundary
(2023) In Advances in Mathematics 420.- 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... (More)
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.
(Less)
- author
- Bandara, Lashi ; Goffeng, Magnus LU and Saratchandran, Hemanth
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Boundary regularity, Calderón projector, Elliptic differential operator, Fredholm boundary conditions
- in
- Advances in Mathematics
- volume
- 420
- article number
- 108968
- publisher
- Elsevier
- external identifiers
-
- scopus:85150766684
- ISSN
- 0001-8708
- DOI
- 10.1016/j.aim.2023.108968
- language
- English
- LU publication?
- yes
- id
- 2dcfafa5-ee1b-43a6-a688-cfb157a4417f
- date added to LUP
- 2023-05-22 11:29:22
- date last changed
- 2023-05-22 11:29:22
@article{2dcfafa5-ee1b-43a6-a688-cfb157a4417f,
abstract = {{<p>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.</p>}},
author = {{Bandara, Lashi and Goffeng, Magnus and Saratchandran, Hemanth}},
issn = {{0001-8708}},
keywords = {{Boundary regularity; Calderón projector; Elliptic differential operator; Fredholm boundary conditions}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Advances in Mathematics}},
title = {{Realisations of elliptic operators on compact manifolds with boundary}},
url = {{http://dx.doi.org/10.1016/j.aim.2023.108968}},
doi = {{10.1016/j.aim.2023.108968}},
volume = {{420}},
year = {{2023}},
}