Year: 2024
Type: article
Abstract: . In this paper we establish a Lebeau–Robbiano spectral inequality for a degenerate one-dimensional elliptic operator, with an optimal dependency with the frequency parameter. The proof relies on a combination of uniform local Carleman estimates away from the degeneracy and a moment method adapted for a degenerate elliptic operator. We also provide an application to the null-controllability on a measurable set in time for the associated degenerate heat equation.
DOI: 10.1137/23m1605211
Authors: Rémi Buffe, Kim Dang Phung, Amine Slimani
Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Institut Élie Cartan de Lorraine, Université de Lorraine, Université de Tours, Université d'Orléans, Institut Denis Poisson, École Nationale Supérieure des Mines de Nancy
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402275648