Analyticity of semigroups generated by higher order elliptic operators in spaces of bounded functions on $C^{1}$ domains

Abstract

This paper shows the analyticity of semigroups generated by higher order divergence type elliptic operators in $L^{\infty}$ spaces in $C^{1}$ domains which may be unbounded. For this purpose, we establish resolvent estimates in $L^{\infty}$ spaces by a contradiction argument based on a blow-up method. Our results yield the $L^{\infty}$ analyticity of solutions of parabolic equations for $C^{1}$ domains.