On the regularity of the principal eigenvalue of the Schrödinger operator on bounded domains

I will present my recent result concerning Lipschitz continuity of the principal eigenvalue of the Schrödinger operator H = - Δ + V on a bounded domain with respect to perturbations of the potential V in Lebesgue spaces. An application to linear stability analysis of stationary solutions of reaction-diffusion equations will be discussed as well.