23 citations · 27 across the 19 of their papers we have counts for
21 papers
The Attribution Blind Spot: Layerwise Trajectory Diagnostics for Source Reliance in Retrieval-Augmented Language Models
Zhe Yu, Wenpeng Xing, Yunzhao Wei +4
A retrieval-augmented model can match a document without relying on it. Controlled knowledge conflicts make source choice observable and let us ask a second question that predictio…
The -regularity conjecture near
Se-Chan Lee, Taehun Lee
We prove the -regularity conjecture in every dimension when is sufficiently close to . To this end, we establish improved Hölder estimates for the gradients of …
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 Ishii…
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 char…
Boundary Hölder gradient estimates for parabolic -Laplace type equations
Se-Chan Lee, Yuanyuan Lian, Hyungsung Yun +1
In this paper, we study the boundary regularity for viscosity solutions of parabolic -Laplace type equations. In particular, we obtain the boundary pointwise regularit…
Time derivative estimates for parabolic -Laplace equations and applications to optimal regularity
Se-Chan Lee, Yuanyuan Lian, Hyungsung Yun +1
We establish the boundedness of time derivatives of solutions to parabolic -Laplace equations. Our approach relies on the Bernstein technique combined with a suitable approximat…
Optimal Hölder regularity for solutions to Signorini-type obstacle problems
Ki-Ahm Lee, Se-Chan Lee, Waldemar Schefer
We study the existence, uniqueness, and regularity of weak solutions to a class of obstacle problems, where the obstacle condition can be imposed on a subset of the domain. In part…
Homogenization of an obstacle problem with highly oscillating coefficients and obstacles
Sunghoon Kim, Ki-Ahm Lee, Se-Chan Lee +1
We develop the viscosity method for the homogenization of an obstacle problem with highly oscillating obstacles. The associated operator, in non-divergence form, is linear and elli…
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…
Regularity for solutions of non-uniformly elliptic equations in non-divergence form
Jongmyeong Kim, Se-Chan Lee
We prove the Aleksandrov--Bakelman--Pucci estimate for non-uniformly elliptic equations in non-divergence form. Moreover, we investigate local behaviors of solutions of such equati…
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…
-regularity for functions in solution classes and its application to parabolic normalized -Laplace equations
Se-Chan Lee, Hyungsung Yun
We establish the global -regularity for functions in solution classes, whenever ellipticity constants are sufficiently close. As an application, we derive the global regu…
-regularity for solutions of degenerate/singular fully nonlinear parabolic equations
Ki-Ahm Lee, Se-Chan Lee, Hyungsung Yun
We establish the interior -estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations For this purpose, we pr…
The Wiener criterion for fully nonlinear elliptic equations
Ki-Ahm Lee, Se-Chan Lee
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 e…
Global regularity results for a class of singular/degenerate fully nonlinear elliptic equations
Sumiya Baasandorj, Sun-Sig Byun, Ki-Ahm Lee +1
We provide the Alexandroff-Bakelman-Pucci estimate and global -regularity for a class of singular/degenerate fully nonlinear elliptic equations. We also derive the existe…
C^{1,α}-regularity for a class of degenerate/singular fully nonlinear elliptic equations
Sumiya Baasandorj, Sun-Sig Byun, Ki-Ahm Lee +1
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 assoc…
The Wiener criterion for nonlocal Dirichlet problems
Minhyun Kim, Ki-Ahm Lee, Se-Chan Lee
We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability and summability . We es…