Thursday, February 24, 2022 - 09:45 in H7 + Zoom
Symmetrization for Fractional Elliptic Problems: A Direct Approach
A talk in the Nonlocal Equations: Analysis and Numerics series by
Vincenzo Ferone from Napoli
| Abstract: |
We provide new direct methods to establish symmetrization results in the form of mass concentration (i.e. integral) comparison for fractional elliptic equations of the type $(-\Delta)^s u = f$ $(0 < s < 1)$ in a bounded domain $\Omega$, equipped with homogeneous Dirichlet boundary conditions. The classical pointwise Talenti rearrangement inequality is recovered in the limit $s \to 1$. Finally, explicit counterexamples constructed for all $s \in (0,1)$ highlight that the same pointwise estimate cannot hold in a nonlocal setting, thus showing the optimality of our results. This is a joint work with Bruno Volzone.
Within the CRC this talk is associated to the project(s): A7 |
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