Homogenization of an eigenvalue problem through rough surfaces

Article type: Research Article

Authors: Avila, Jake^a | Monsurrò, Sara^{b; *} | Raimondi, Federica^b

Affiliations: [a] Institute of Mathematics, University of the Philippines Diliman, 1101 Diliman (Quezon City), Philippines | [b] Department of Mathematics, University of Salerno, 84084 Fisciano (Salerno), Italy

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In a bounded cylinder with a rough interface we study the asymptotic behaviour of the spectrum and its associated eigenspaces for a stationary heat propagation problem. The main novelty concerns the proof of the uniform a priori estimates for the eigenvalues. In fact, due to the peculiar geometry of the domain, standard techniques do not apply and a suitable new approach is developed.

Keywords: Eigenvalue problem, homogenization, rough surfaces, interface conditions

DOI: 10.3233/ASY-231882

Journal: Asymptotic Analysis, vol. 137, no. 1-2, pp. 97-121, 2024