Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter

Article type: Research Article

Authors: Gittins, K.^{a; *} | Helffer, B.^b

Affiliations: [a] Department of Mathematical Sciences, Durham University, Lower Mountjoy, DH1 3LE Durham, United Kingdom | [b] Laboratoire de Mathématiques Jean Leray, Université de Nantes, 2 rue de la Houssinière, 44 322 Nantes CEDEX 3, France. E-mail: [email protected]

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

Abstract: We consider the cases where there is equality in Courant’s nodal domain theorem for the Laplacian with a Robin boundary condition on the square. In our previous two papers, we treated the cases where the Robin parameter h>0 is large, small respectively. In this paper we investigate the case where h<0.

Keywords: Courant-sharp, Robin eigenvalues, negative parameter, squar

DOI: 10.3233/ASY-201642

Journal: Asymptotic Analysis, vol. 124, no. 1-2, pp. 69-107, 2021