Inverse problems for semilinear elliptic PDE with measurements at a single point

Autor:	Salo, Mikko, Tzou, Leo
Rok vydání:	2023
Předmět:	osittaisdifferentiaaliyhtälöt Mathematics - Analysis of PDEs Applied Mathematics General Mathematics FOS: Mathematics Mathematics::Analysis of PDEs Mathematics::Spectral Theory inversio-ongelmat Analysis of PDEs (math.AP)
Zdroj:	Proceedings of the American Mathematical Society.
ISSN:	1088-6826 0002-9939
Popis:	We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the Dirichlet-to-Neumann map measured at a single boundary point, or integrated against a fixed measure. This result is valid even when the Dirichlet data is only given on a small subset of the boundary. We also give related uniqueness results on Riemannian manifolds. 14 pages, added the reference [CGU21] in v2
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd308a71360202c66c07926fd7b70764 https://doi.org/10.1090/proc/16255 Zobrazit plný text záznamu