The Calderón problem for the conformal Laplacian

Autor:	Lassas, Matti, Liimatainen, Tony, Salo, Mikko
Rok vydání:	2022
Předmět:	osittaisdifferentiaaliyhtälöt Riemannin monistot Statistics and Probability Geometry and Topology Statistics Probability and Uncertainty inversio-ongelmat Analysis
Zdroj:	Communications in Analysis and Geometry. 30:1121-1184
ISSN:	1944-9992 1019-8385
DOI:	10.4310/cag.2022.v30.n5.a6
Popis:	We consider a conformally invariant version of the Calderón problem, where the objective is to determine the conformal class of a Riemannian manifold with boundary from the Dirichlet-to-Neumann map for the conformal Laplacian. The main result states that a locally conformally real-analytic manifold in dimensions can be determined in this way, giving a positive answer to an earlier conjecture [LU02, Conjecture 6.3]. The proof proceeds as in the standard Calderón problem on a real-analytic Riemannian manifold, but new features appear due to the conformal structure. In particular, we introduce a new coordinate system that replaces harmonic coordinates when determining the conformal class in a neighborhood of the boundary. peerReviewed
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0c07cc0ec1577ebf76c1a692b000f6ac https://doi.org/10.4310/cag.2022.v30.n5.a6 Zobrazit plný text záznamu