The fundamental gap for a one-dimensional Schrödinger operator with Robin boundary conditions

Ben Andrews, Julie Clutterbuck, Daniel Hauer

Abstract

For Schrödinger operators on an interval with either convex or symmetric, single-well potentials, and Robin or Neumann boundary conditions, the gap between the two lowest eigenvalues is minimised when the potential is constant. We also have results for the \(p\)-Laplacian.

Keywords: Eigenvalue problem, Robin boundary condition, fundamental gap, p-Laplacian.

AMS Subject Classification: Primary 47A75; secondary 34B09, 34B15, 34L15, 34L40.