On the persistence of the multiplicity of eigenvalues for some variational elliptic operator depending on the domain (Q1900405)

The authors consider an elliptic eigenvalue problem \[ Lu= \lambda u\quad\text{in} \quad \Omega,\quad u= 0\quad\text{on} \quad\partial\Omega \] and assume that for a given domain \(\Omega\) it admits an eigenvalue of multiplicity 2. They then study under which conditions a domain perturbation preserves the multiplicity 2; however there is no description of the geometry of the domain for which their results hold.