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

This paper shows the analyticity of semigroups generated by higher order divergence type elliptic operators in L∞ spaces when the domain has only C regularity. The domain can be unbounded. For this purpose we establish resolvent estimates in L∞ spaces by a contradiction argument based on a blow up argument. Our results yield the L∞ analyticity of solutions of parabolic equations for C domains. Keywards: Higher order elliptic operator, Analytic semigroup, L∞ estimate, C domain, Blow up argument. Mathematics Subject Classification(2010). 35J40