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

開催日時
2016年   1月 12日 16時 30分 ~ 2016年   1月 12日 17時 30分
場所
北海道大学理学部3号館3-309室
講演者
鈴木 拓也 氏 (東京大学)
 
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.

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