Elliptic Regularity for BVP with Robin boundary conditions

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The Elliptic Regularity Theorem in this text (http://www.ma.utexas.edu/users/arbogast/appMath08c.pdf, Pg 223, Theorem 8.13) is only stated for pure Dirichlet or pure Neumann BVPs.

I was wondering if this result also holds for pure Robin BVPs, and what the form of the bounds on $||u||_{H^{k+2}(\Omega)}$ are for the Robin case ?