数学科学研究所
Insitute of Mathematical Science

Colloquium: The Dirichlet Problem for the Logarithmic Laplacian

Colloquium| Institute of Mathematical Sciences

Time14:00-15:00, November 21 Thursday

LocationRoom S408, IMS

 

Speaker:  Chen Huyan, New York University Shanghai

Abstract:  In this talk, we study the logarithmic Laplacian operator L, which is a singular integral operator with symbol 2log|ζ|. We show that this operator has the integral representation

with) and , where Γ is the Gamma function, is the Digamma function and (1) is the Euler Mascheroni constant. This operator arises as formal derivative of fractional Laplacians at s = 0. We develop the functional analytic framework for Dirichlet problems involving the logarithmic Laplacian on bounded domains and use it to characterize the asymptotics of principal Dirichlet eigenvalues and eigenfunctions of (−∆)s as s → 0.




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