Search
Talk

Variations on the Logarithmic Laplacian Operator

  • Tobias Weth (Goethe-Universität Frankfurt)
A3 01 (Sophus-Lie room)

Abstract

The Logarithmic Laplacian Operator arises as formal derivative of fractional Laplacians at order s= 0. In this talk I will discuss properties of this operator and its relevance in the derivation of asymptotics of Dirichlet eigenvalues and eigenfunctions of fractional Laplacians in bounded domains as the order tends to zero. A further applications arises in the study of the monotonicity of solutions to fractional Poisson problems with respect to the fractional order s. As a byproduct of this study, we derive explicit bounds for the corresponding Green operator on arbitrary bounded domains which seem to be new even for the case s=1, i.e., for the classical local Dirichlet problem −Δu=f in Ω, u≡0 on ∂Ω.

This is joint work with Huyuan Chen, Sven Jarohs and Alberto Saldana.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss