On the eigenvalues of the biharmonic operator on annuli

2025/10/06 by Buoso, Davide, Molinarolo, Riccardo
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.04809

Abstract

We show that the fundamental tone of the bilaplacian with Dirichlet or Navier boundary conditions on radially symmetric domains is always simple in dimension N≥3. In dimension N=2 we show that it is simple if the inner radius is big enough.

Citations

• Sharp inequalities and asymptotics for polyharmonic eigenvalues
• Bulk-Boundary eigenvalues for Bilaplacian problems
• The Bilaplacian with Robin boundary conditions

Related

• Analyticity and criticality results for the eigenvalues of the biharmonic operator
• Neumann eigenvalues of the biharmonic operator on domains: geometric bounds and related results
• The Bilaplacian with Robin boundary conditions
• Bulk-Boundary eigenvalues for Bilaplacian problems
• An annulus and a half-helicoid maximize Laplace eigenvalues