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

2020/03/25 by Katie Gittins, Bernard Helffer, Gittins, Katie +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2003.11304

Abstract

We consider the cases where there is equality in Courant's nodal domain\ntheorem for the Laplacian with a Robin boundary condition on the square. In our\nprevious two papers, we treated the cases where the Robin parameter h>0 is\nlarge, small respectively. In this paper we investigate the case where h<0 ,.\n

Related

• Courant-sharp Robin eigenvalues for the square -- the case with small Robin parameter--
• Courant-sharp Robin eigenvalues for the square and other planar domains
• Nodal counts for the Robin problem on Lipschitz domains
• Upper bounds for Courant-sharp Neumann and Robin eigenvalues
• Nodal domains in the square---the Neumann case