儀我 美一

講演題目

連続関数の空間での偏微分方程式

Partial differential equations in a space of continuous functions

英文サマリ

A space of continuous functions is a simple and naive class of functions. However, it is often difficult to handle partial differential equations (PDEs) in such a class of functions. For an equation having an order-preserving structure, the theory of viscosity solutions allows us to handle PDEs in a space of continuous functions. In this talk, as an application of the theory, we discuss a level-set method for the mean curvature flow with prescribed boundary. However, for a system of equations, we often lose the order-preserving property. Nevertheless, in some cases, we are still able to measure regularizing effects in a space of continuous functions. In this talk, we explain the regularizing effects for the Stokes system, which is a linearized Navier-Stokes system.