Monday, March 17, 2025 - 11:40 in V2-205
Removable singularities for nonlocal equations and nonlocal minimal graphs
A talk in the Nonlocal Equations: Analysis and Numerics series by
Minhyun Kim from Seoul
| Abstract: |
In this talk, we study the local behavior of solutions, with possible singular-
ities, of nonlocal nonlinear equations modeled on the fractional p-Laplace
equation $(1 < p < \infty)$ and nonlocal minimal surface equation (which
corresponds to the case $p = 1$).
For the case $1 < p < \infty$, we first prove that sets of fractional capacity zero
are removable for solutions under certain integrability conditions. We then
characterize the asymptotic behavior of singular solutions near an isolated
singularity in terms of the fundamental solution. This result is based on
joint work with Se-Chan Lee.
For the case $p = 1$, we show that any nonlocal minimal graph in $\Omega \setminus K$,
where $\Omega \subset \mathbb{R}^n$ is an open set and $K \subset \Omega$ is a compact set of $(s, 1)$-capacity zero, is indeed a nonlocal minimal graph in all of $\Omega$.
Within the CRC this talk is associated to the project(s): A7 |
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