非线性分析研讨班：Sharp Lp estimates and size of nodal sets of generalized Steklov eigenfunctions

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：张城 (清华大学)

题  目：Sharp Lp estimates and size of nodal sets of generalized Steklov eigenfunctions

时  间：2023.03.30（星期四）10:30-11:30

地  点：思源楼S817

摘  要：We prove sharp Lp estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their L2 norms on the boundary. We prove it by establishing Lp bounds for the harmonic extension operators as well as the spectral projection operators on the boundary. Moreover, we derive lower bounds on the size of nodal sets for a variation of the Steklov spectral problem. We consider a generalized version of the Steklov problem by adding a non-smooth potential on the boundary but some of our results are new even without potential. This is a joint work with X. Huang(Maryland), Y. Sire(Johns Hopkins) and X. Wang(Hunan U)