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.
Citation
Takuya Suzuki. "Analyticity of semigroups generated by higher order elliptic operators in spaces of bounded functions on $C^{1}$ domains." Adv. Differential Equations 22 (9/10) 593 - 620, September/October 2017. https://doi.org/10.57262/ade/1495850455
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