丘成桐中心几何与方程组讨论班
SEU Yau Center Geometry and PDE Seminar
Title: Quantitative unique continuation property for solutions to a bi-Laplacian equation with a potential
Speaker: Hairong Liu（刘海蓉）
Affiliation: Nanjing University of Science and Technology (南京理工大学)
Time: 09:00-10:00 am, 15th May (Thurs.), 2025 (GMT+8)
Venue: Room 1502, Shing-Tung Yau Center, Yifu Architecture Building, Sipailou Campus of Southeast University, Nanjing
（东南大学四牌楼校区逸夫建筑馆丘成桐中心1502室）
Inviter: Feida Jiang（蒋飞达）
Abstract:
In this talk, we will show the quantitative unique continuation property of solutions to a bi-Laplacian equation with a potential. Our key argument is to lift the original equation to that with a positive potential, then decompose the resulted fourth-order equation into a special system of two second-order equations. Based on the special system, we define a variant frequency function with weights and derive its almost monotonicity to establishing some doubling inequalities with explicit dependence on the Sobolev norm of the potential function.
Speaker:
刘海蓉，南京理工大学数学与统计学院教授、博士生导师。主要从事几何和物理中偏微分方程理论及其应用研究，在椭圆方程解的定量性质，次黎曼流形上向量场方程解的性态等方面取得多项研究成果，相关工作发表在JFA, JDE, Nonlinearity，SCM等数学杂志上。主持国家自然科学基金青年基金、国家自然科学基金面上项目、国家自然科学基金天元专项等项目。