dc.contributor.author | Alibaud, Nathael | |
dc.contributor.author | del Teso, Félix | |
dc.contributor.author | Endal, Jørgen | |
dc.contributor.author | Jakobsen, Espen Robstad | |
dc.date.accessioned | 2020-09-18T06:47:55Z | |
dc.date.available | 2020-09-18T06:47:55Z | |
dc.date.created | 2020-09-02T08:35:54Z | |
dc.date.issued | 2020 | |
dc.identifier.issn | 0021-7824 | |
dc.identifier.uri | https://hdl.handle.net/11250/2678357 | |
dc.description.abstract | A result by Courrège says that linear translation invariant operators satisfy
the maximum principle if and only if they are of the form L = Lσ,b + Lμ
where
Lσ,b[u](x) = tr(σσTD2u(x)) + b · Du(x)
and
Lμ[u](x) =
Rd\{0}
u(x + z) − u(x) − z · Du(x)1|z|≤1
dμ(z).
This class of operators coincides with the infinitesimal generators of Lévy processes
in probability theory. In this paper we give a complete characterization of the
operators of this form that satisfy the Liouville theorem: Bounded solutions u of
L[u] = 0 in Rd are constant. The Liouville property is obtained as a consequence of
a periodicity result that completely characterizes bounded distributional solutions
of L[u] = 0 in Rd. The proofs combine arguments from PDEs and group theory.
They are simple and short. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Elsevier | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | The Liouville theorem and linear operators satisfying the maximum principle. | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | publishedVersion | en_US |
dc.source.journal | Journal des Mathématiques Pures et Appliquées | en_US |
dc.identifier.doi | 10.1016/j.matpur.2020.08.008 | |
dc.identifier.cristin | 1826624 | |
dc.relation.project | Norges forskningsråd: 250070 | en_US |
dc.description.localcode | © 2020 The Authors. Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). | en_US |
cristin.ispublished | false | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |