## 偏微分方程式セミナー(2016/1/12): On the elliptic resolvent estimates in spaces of bounded functions, 鈴木 拓也 氏

2016年 　 1月 12日 16時 30分 ～ 2016年 　 1月 12日 17時 30分

We mainly consider the resolvent problems for higher order elliptic operators with the Dirichlet condition in $L^{\infty}$ spaces when the domain has only $C^{1}$ regularity. The typical examples of higher order elliptic operators are the Laplace operator, bi-Laplace operator, and these operators with coefficient functions as inhomogeneous medium. Our argument is a contradiction argument based on a blow up argument without appealing the Masuda-Stewart method. Our results yield the existence, uniqueness, and analyticity of solutions of parabolic equations in $L^{\infty}$ space for $C^{1}$ domains. Moreover, we will introduce joint works for the Stokes resolvent problems with Professor Ken Abe, Professor Yosikazu Giga, and Dr. Katharina Schade as related topics.