Stability of square root domains associated with elliptic systems of PDEs on nonsmooth domains

Abstract

We discuss stability of square root domains for uniformly elliptic partial differential operators La,Ω,Γ=−∇⋅a∇ in L2(Ω), with mixed boundary conditions on ∂Ω, with respect to additive perturbations. We consider open, bounded, and connected sets Ω∈Rn, n∈N\\{1}, that satisfy the interior corkscrew condition and prove stability of square root domains of the operator La,Ω,Γ with respect to additive potential perturbations V∈Lp(Ω)+L∞(Ω), p>n/2.Special emphasis is put on the case of uniformly elliptic systems with mixed boundary conditions.