威廉希尔学术报告

--- 分析与偏微分方程讨论班(2023秋季第10讲)

Sobolev Homeomorphic Extensions

Aleksis Koski博士

(Aalto University; Finland)

时间与地点：2023年11月1日（周三）15:00-16:00（北京时间);

Zoom Meeting: https://jyufi.zoom.us/j/69995645035;

会议号：699 9564 5035

摘要: One of the most fundamental results in complex analysis is the Riemann Mapping Theorem, which provides a way to express domains in the plane as conformal images of the unit disk. Much in the same spirit, one can ask which properties of a fixed boundary map allow for a homeomorphic extension with specific geometric and analytic properties. In Nonlinear Elasticity, the existence of a Sobolev homeomorphism between two given shapes constitutes an axiomatic property for the associated minimization problems to be well-defined. Classical results such as the Beurling-Ahlfors extension theorem or the Radó-Kneser-Choquet theorem provide the basic building blocks to address these questions in the 2D case, but do not extend well to irregular domains or to higher dimensions. In this talk, I will review these problems starting from the basics and introduce the methods we have developed in recent years together with Jani Onninen and Stanislav Hencl to address both 2D and 3D extension problems.

报告人简介: Aleksis Koski, 几何函数论领域知名青年专家，博士毕业于芬兰赫尔辛基大学，师从国际著名几何函数论领域专家Tadeusz Iwaniec，目前就职于芬兰Aalto University，已在JEMS、Adv. Math、ARMA、JMPA、JFA、CVPDE等著名期刊发表高水平学术文章十余篇。

邀请人：朱政

欢迎大家参加！