PDE Seminar (2016/1/12): On the elliptic resolvent estimates in spaces of bounded functions

2016-1-12 16:30 - 2016-1-12 17:30
Faculty of Science Building #3, Room 309
Takuya Suzuki (The University of Tokyo)
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 Mr. Ken Abe, Professor Yosikazu Giga, and Ms. Katharina Schade as related topics.