4 papers · 1 filter
Liouville theorem for singular solutions to nonlocal equations
Minhyun Kim, Se-Chan Lee
We study singular solutions to the fractional Laplace equation and, more generally, to nonlocal linear equations with measurable kernels. We establish Bôcher type results that char…
Singularities of solutions of nonlocal nonlinear equations
Minhyun Kim, Se-Chan Lee
We study the local behavior of weak solutions, with possible singularities, of nonlocal nonlinear equations. We first prove that sets of capacity zero are removable for weak soluti…
Wolff potential estimates and Wiener criterion for nonlocal equations with Orlicz growth
Minhyun Kim, Ki-Ahm Lee, Se-Chan Lee
We prove the Wolff potential estimates for nonlocal equations with Orlicz growth. As an application, we obtain the Wiener criterion in this framework, which provides a necessary an…
Supersolutions and superharmonic functions for nonlocal operators with Orlicz growth
Minhyun Kim, Se-Chan Lee
We study supersolutions and superharmonic functions related to problems involving nonlocal operators with Orlicz growth, which are crucial tools for the development of nonlocal non…