非线性分析研讨班:On some variational problems with vanishing mean condition over boundary

中科院数学与系统科学研究院

数学研究所

学术报告

非线性分析研讨班

报告人：李沁峰 （湖南大学）

题  目：On some variational problems with vanishing mean condition over boundary

时  间：2024.1.15（星期一）上午10:30-11:30

地  点：思源楼615

摘  要：We will introduce the Neumann torsion and boundary mean zero Laplacian eigenvalue problem. First, for the Neumann torsional energy, we prove that ball is local minizer among smooth perturbations, but not a local minimizer among Lipscthiz perturbations. This is a rather suprising result in view of rigidity results of Dirichlet and Robin torsional enery.  Second, we discuss stability of Serrin's system related to Neumann torsion function. Third, we prove spectral inequalities and some isoperimetric inequalities on special domains on boundary mean zero Laplacian eigenvalue. Many open questions will be given along the talk, in terms of how geometry of domain affect distribution of state functions.