Abstract: I would like to talk on the outlined theory of maximal regularity on the simplest parabolic equations such as the heat equation and the Stokes equations in the limiting function class BMO (bounded mean oscillations). Maximal regularity for the Cauchy problem of parabolic equations is well-understood in the UMD Banach spaces. If the Banach space is UMD, then it is necessarily reflexive, Maximal regularity in non-reflexive space is exceptional case and it is required for an individual treatment to establish a related estimate. After introducing some basic facts on the functions in BMO, I will show maximal regularity holds for the solution to the Cauchy problem of the heat equation and the Stokes equations in BMO space. This talk is based on the joint work with Senjo Shimizu (Kyoto University). The following is the contents:
1．Introducation for maximal regularity
2．Motivation and main result
3．Basic properties of BMO
4．Extended John-Nirenberg theorem and singular integral operators
5．The homogeneous estimate by Koch-Tataru
6．Proof of main result.
7．Some applications
Zoom Information:
https://zoom.us/j/95451435768?pwd=Rlh0WVIvR241cEg5L0sycjkrZ3ZQZz09
ID： 954 5143 5768
PW：786525
