数学研究所
数学科学全国重点实验室

学术报告

偏微分方程研讨班

Speaker: 陈虎元 教授 （上海数学与交叉学科研究院）

Inviter: 邱国寰

Language: Chinese

Title: On differential equations involving the Logarithmic Laplacian

Time&Venue: 2025年7月16日（星期三）10:00-11:00&思源楼S625

Abstract: In this presentation, we investigate the logarithmic Laplacian operator, a singular integral operator characterized by the symbol \(2\log |.|\). We establish that this operator admits an integral representation. This operator emerges as the formal derivative of fractional Laplacians at the origin.We show the Dirichlet eigenvalues for the logarithmic Laplacian on bounded domains,  show heat kernels, and solutions to the Cauchy problem and positive solutions of Semilinear Critical elliptic problems in the whole domain.