杜力力教授学术报告

报告题目：The free boundary for the singular obstacle problem with logarithmic forcing term

报 告 人：杜力力 教授

负 责 人：陈文晶

报告时间：2024年12月15日（星期日）15:00-16:00

报告地点：数学大楼322

参加人员：教师、研究生、本科生

报告摘要：In this talk, we will introduce a class of singular obstacle-type free boundary problem with logarithmic forcing term. The main results give the regularity of the free boundary for the obstacle-type problem. The logarithmic forcing term becomes singular near the free boundary and lacks the scaling properties, which are very crucial in studying the regularity of the free boundary. Despite these challenges, we draw inspiration for our overall strategy from the epiperimetric inequality method introduced by G. Weiss in 1999 [Invent. Math., 138, 1999]. Central to our approach is the introduction of a new type of energy contraction. This allows us to achieve energy decay, which in turn ensures the uniqueness of the blow-up limit, and subsequently leads to the regularity of the free boundary.

报告人简介：杜力力，教授，博士生导师。从事非线性偏微分方程及其应用的研究工作，在高维可压缩Euler方程组的适定性、Bernoulli型自由边界问题等研究领域取得了一系列的结果，在Arch. Rational Mech. Anal., Comm. Math. Phys., Tran. AMS., Comm. PDEs等国际学术刊物发表学术论文 60余篇。2014年获四川省杰出青年基金，2016年获国家优秀青年科学基金，2017年入选教育部国家级人才青年学者，2018年入选四川省学术和技术带头人，2021年获国家杰出青年科学基金。2021年获得四川省数学会首届（2020年度）基础数学奖一等奖（唯一完成人）。