湖南大学偏微分方程研讨会

会议时间：2021/11/06 14:00-18:30 (GMT+08:00) 中国标准时间 - 北京

会议腾讯ID：782 134 940

2021/11/06 14:00-14:45

报告人：唐岚 华中师范大学

报告题目：Free boundary problem for the obstacle problem of Monge-Ampere Equation

报告摘要：We establish regularity theory for free boundary of the obstacle problem to the Monge-Ampere equations. This is a joint work with Genggeng Huang and Xujia Wang.

2021/11/06 14:45-15:30

报告人：代国伟 大连理工大学

报告题目：Bifurcation theory of nonlinear operator equations and its applications

报告摘要：This talk contains four parts. In the first part, we present some new global bifurcation theorems of nonlinear operator equations. In the second part, we mainly introduce the method of branches approximating. In the third part, we present some new results about interval bifurcation. In the last part, we give several applications of the above new theory and methods.

2021/11/06 15:30-16:15

报告人：郭千桥 西北工业大学

报告题目：Multi-bubble nodal solutions to slightly subcritical elliptic problems with Hardy terms

报告摘要：The paper is concerned with the slightly subcritical elliptic problem with Hardy term

in a bounded domain  with , in dimensions . We prove the existence of multi-bubble nodal solutions that blow up positively at the origin and negatively at a different point as and  with . In the case of  being a ball centered at the origin we can obtain solutions with up to 5 bubbles of different signs. We also obtain nodal bubble tower solutions, i.e. superpositions of bubbles of different signs, all blowing up at the origin but with different blow-up order. The asymptotic shape of the solutions is determined in detail. This is a joint work with Professor Thomas Bartsch.

2021/11/06 16:15-17:00

报告人：熊金钢 北京师范大学

报告题目：Optimal regularity for fast diffusion equations in bounded domains

报告摘要：I will report my recent joint work with T. Jin, in which we prove optimal global regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains. In particular, we solve a problem raised by Berryman and Holland in 1980.