Bounds on the multiplicity of eigenvalues for fixed membranes. (English) Zbl 0949.35102
The authors prove that the multiplicity of the \(k\)th eigenvalue of a membrane in the plane is not greater than \(2k-3\), \(k\geq 3\). This improves the earlier result of N. Nadirashvili [Math. USSR Sb. 61, No. 1, 225-238 (1988; Zbl 0672.35049)], who showed the bound \(2k-1\).
Reviewer: N.Jacob (Erlangen)
MSC:
| 35P20 | Asymptotic distributions of eigenvalues in context of PDEs |
| 35P15 | Estimates of eigenvalues in context of PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
