Extremal eigenvalue gaps for the Schrödinger operator with Dirichlet boundary conditions
Samir Karaa · Journal of Mathematical Physics · 1998
We consider the problems of minimizing and maximizing the gap between the two lowest Dirichlet eigenvalues of the Schrödinger operator −Δ+V(x) on a bounded domain in Rn, when the potential V is subjected to a p-norm constraint. We give characterization theorems for extremizing potentials. We prove in particular that a second eigenvalue corresponding to a minimizing potential is always single.