## Advances in Differential Equations

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

Takuya Suzuki

#### 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.

#### Article information

Source
Adv. Differential Equations Volume 22, Number 9/10 (2017), 593-620.

Dates
First available in Project Euclid: 27 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ade/1495850455

#### Citation

Suzuki, Takuya. Analyticity of semigroups generated by higher order elliptic operators in spaces of bounded functions on $C^{1}$ domains. Adv. Differential Equations 22 (2017), no. 9/10, 593--620. https://projecteuclid.org/euclid.ade/1495850455