Article ID Journal Published Year Pages File Type
4610037 Journal of Differential Equations 2015 16 Pages PDF
Abstract

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

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Physical Sciences and Engineering Mathematics Analysis
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