arXiv subjects

Se-Chan Lee

Publications and source records attributed to Se-Chan Lee.

22 records · Page 2Linked to original sources

arXiv2023

The Wiener criterion for fully nonlinear elliptic equations

We study the boundary continuity of solutions to fully nonlinear elliptic equations. We first define a capacity for operators in non-divergence form and derive several capacitary estimates. Secondly, we formulate the Wiener criterion, which characterizes a regular boundary point via potential theory. Our approach utilizes the asymptotic behavior of homogeneous solutions, together with Harnack inequality and the comparison principle.

math.AP↗

arXiv2022

Global regularity results for a class of singular/degenerate fully nonlinear elliptic equations

We provide the Alexandroff-Bakelman-Pucci estimate and global $C^{1, α}$-regularity for a class of singular/degenerate fully nonlinear elliptic equations. We also derive the existence of a viscosity solution to the Dirichlet problem with the associated operator.

math.AP↗

arXiv2022

C^{1,α}-regularity for a class of degenerate/singular fully nonlinear elliptic equations

We establish an optimal C^{1,α}-regularity for viscosity solutions of degenerate/singular fully nonlinear elliptic equations by finding minimal regularity requirements on the associated operator.

math.AP↗

arXiv2022

The Wiener criterion for nonlocal Dirichlet problems

We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability $s \in (0, 1)$ and summability $p>1$. We establish a nonlocal counterpart of the Wiener criterion, which characterizes a regular boundary point in terms of the nonlocal nonlinear potential theory.

math.AP↗