10 papers
Capacitary estimates for solutions to nonlocal Dirichlet problems
Minhyun Kim, Se-Chan Lee, Marvin Weidner
We study the boundary regularity of weak solutions to nonlocal nonlinear elliptic equations with bounded measurable coefficients. Our main result establishes that a capacity densit…
A priori estimates for solutions of degenerate fully nonlinear elliptic equations with data
Hongsoo Kim, Se-Chan Lee
We establish a priori regularity estimates for viscosity solutions of degenerate fully nonlinear elliptic equations with integrable right-hand sides. When the nonhomogeneous term b…
Quantitative bounds for Hölder exponents in the Krylov--Safonov and Evans--Krylov theories
Jongmyeong Kim, Se-Chan Lee
We establish quantitative bounds for Hölder exponents in the Krylov--Safonov and Evans--Krylov theories when the ellipticity ratio is close to one. Our analysis relies on the Ishi…
Nonlocal Harnack inequality in a disconnected region
Se-Chan Lee
We establish a Harnack inequality for weak solutions of nonlocal equations in a disconnected region. The inequality compares the value of a solution on one connected component with…
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 cha…
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…