R-sectoriality of higher-order elliptic systems on general bounded domains

On bounded domains , reaching far beyond the scope of Lipschitz domains, we consider an elliptic system of order 2m in divergence form with complex -coefficients complemented with homogeneous mixed Dirichlet/Neumann boundary conditions. We prove that the -realization of the corresponding operator A is -sectorial of angle , where in the case , , and where for some in the case . To perform this proof, we generalize the -extrapolation theorem of Shen to the Banach space-valued setting and to arbitrary Lebesgue-measurable underlying sets.