理学院学术报告：Existence of solutions with isolated singularity for a semilinear

报告题目：Existence of solutions with isolated singularity for a semilinear Helmholtz equation

报 告 人：周风教授

报告时间：2023年11月5日（星期日） 16：30—17：30

报告地点：5B-307

报告人简介：

周风，华东师范大学数学科学学院教授，博士生导师，中国数学会常务理事。1993年获得巴黎第六大学数学博士学位，师从H. Brezis教授。2004年至2012年任华东师范大学数学系系主任。入选上海市曙光计划、上海市优秀学科带头人计划，主持国家“数学创新引智”计划。研究领域为非线性偏微分方程，主要研究几何、数学物理中若干非线性偏微分方程解的性态及相关问题。研究成果发表在Comm. Pure Appl. Math., J. Funct. Anal.,  Ann. I.H.P.，Calc. Var. PDEs., J. Differential Equations等国际著名数学期刊上。

报告摘要：

In this talk, we review some basic properties for Helmholtz operator and an appropriate classification of Helmholtz harmonic functions is involved according to the asymptotic behavior at infinity. We discuss the isolated singular solutions of a semilinear Helmholtz equation. In particular, we give the classification of the isolated singularity in the Serrin's subcritical case. The isolated singular solutions is then derived via the Schauder’s fixed point theorem for the corresponding integral equation. The talk is based on joint work with H.Y. Chen.