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

We discuss stability of square root domains for uniformly elliptic partial differential operators $L_{a,\mathrm{\Omega },\mathrm{\Gamma }}=-\mathrm{\nabla }\cdot a\mathrm{\nabla }$ in $L^2(\mathrm{\Omega })$, with mixed boundary conditions on $\mathrm{\partial }\mathrm{\Omega }$, with respect to additive perturbations. We consider open, bounded, and connected sets $\mathrm{\Omega }\in {\mathbb{R}}^n$, $n\in \mathbb{N}\mathrm{\backslash }\{1\}$, that satisfy the interior corkscrew condition and prove stability of square root domains of the operator $L_{a,\mathrm{\Omega },\mathrm{\Gamma }}$ with respect to additive potential perturbations $V\in L^p(\mathrm{\Omega })+L^{\mathrm{\infty }}(\mathrm{\Omega })$, $p>n\mathrm{/}2$. Special emphasis is put on the case of uniformly elliptic systems with mixed boundary conditions.