Wednesday, February 23, 2022 - 14:30 in H7 + Zoom
Douglas identities in $L^p$
A talk in the Nonlocal Equations: Analysis and Numerics series by
Artur Rutkowski from Wrocław
| Abstract: |
In his study of Plateau's problem, J. Douglas established an identity which connects the Dirichlet energy of a harmonic function in the planar unit disk with the $H^{1/2}$-type energy of its boundary values. It turns out that such a formula can also be obtained for other domains, and the harmonic functions of operators $L$ other than the Laplacian, e.g., nonlocal Lévy operators. Our goal is to show how to develop these types of identities in the $L^p$ setting. Instead of the standard Dirichlet energy $(Lu,u)$, we use functionals of the form $(Lu,|u|^{p-1}{ sgn\,} u)$.
The talk is based on joint works with Krzysztof Bogdan, Damian Fafuła, Tomasz Grzywny, and Katarzyna Pietruska-Pałuba.
Within the CRC this talk is associated to the project(s): A7 |
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