Thursday, March 21, 2024 - 14:00 in V3-201
Optimal boundary regularity for nonlocal elliptic equations
A talk in the Other series by
Marvin Weidner from Barcelona
| Abstract: |
In this talk we discuss the boundary regularity for solutions to nonlocal elliptic equations. A main focus of the talk will be on our recent result, where we establish that solutions are C^s up to the boundary whenever the kernel is comparable to the one of the fractional Laplacian. This result was known to hold only for homogeneous kernels, and it is quite surprising that it holds for inhomogeneous kernels, too.
The key new idea is to construct a 1D solution as a minimizer of an appropriate nonlocal one-phase free boundary problem, for which we establish optimal regularity and non-degeneracy estimates.
This talk is based on a joint work with Xavier Ros-Oton (https://arxiv.org/abs/2403.07793)
Within the CRC this talk is associated to the project(s): A7 |
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