On the number of Courant-sharp Dirichlet eigenvalues
  We consider arbitrary open sets $\Omega$ in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of $\Omega$, (ii) the number of Courant-sharp Dirichlet eigenvalues of $\Omega$. This extends recent results of P. B\'erard and B. Helffer. 
Michiel van den Berg, Katie Gittins
math.SP math.AP