Friday, February 25, 2022 - 09:00 in H7 + Zoom
The fractional Poisson problem and the logarithmic Laplacian
A talk in the Nonlocal Equations: Analysis and Numerics series by
Tobias Weth from Frankfurt
| Abstract: |
I will discuss some recent results on the family of fractional Poisson problems $(-\Delta)^s u = f$ in $\Omega$, $ u = 0$ on $\Omega^c$ of order $2s$ and its connection to the logarithmic Laplacian operator. This connection allows, in particular, to characterize the $s$-dependence of solutions to this family. Special attention will be given to the case $f\equiv 1$, i.e., the fractional torsion problem. As a byproduct of our study, we derive new bounds for the corresponding Green operators on arbitrary bounded domains. This is joint work with Sven Jarohs and Alberto Saldana.
Within the CRC this talk is associated to the project(s): A7 |
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