Sun-Sig Byun

Gradient Estimates Near the Natural Exponent for Very Weak Solutions to $A_{p}$ -Weighted Quasilinear Elliptic Equations

Sun-Sig Byun, Minkyu Lim

We establish local Calderón--Zygmund estimates near the natural exponent for very weak solutions to matrix-weighted quasilinear equations\[ - \mathrm{div\,} A_{\mathbb{M}}(x,Du) =…

Calderon-Zygmund estimates for generalized double phase equations with matrix weights

Sun-Sig Byun, Hongsoo Kim

We prove Calderon-Zygmund estimates for generalized double phase equations with Orlicz growth and variable matrix weights. The operator combines a non-uniformly elliptic double pha…

C^{1,α} regularity for a class of singular/degenerate fully nonlinear elliptic equations with oblique boundary conditions

Sun-Sig Byun, Hongsoo Kim, Seunghyun Kim

In this paper, we establish global $C^{1, α}$ regularity for viscosity solutions to a class of singular and degenerate fully nonlinear elliptic equations subject to oblique boundar…

Harnack inequality for anisotropic fully nonlinear equations with nonstandard growth

Sun-Sig Byun, Hongsoo Kim

We establish Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear anisotropic elliptic equations with nonstandard growth, including anisotropic-$(p…

Regularity for fully nonlinear elliptic equations in generalized Orlicz spaces

Sun-Sig Byun, Jeongmin Han, Mikyoung Lee

In this paper, we establish an optimal global Calderón-Zygmund type estimate for the viscosity solution to the Dirichlet boundary problem of fully nonlinear elliptic equations with…

ABP estimate and Harnack inequality for a class of degenerate fully nonlinear pseudo- $p$ -Laplacian equations

Sun-Sig Byun, Hongsoo Kim

We prove Aleksandrov-Bakelman-Pucci estimates and Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear pseudo- $p$ -Laplacian equations in nondiverge…

Lipschitz regularity for anisotropic fully nonlinear equations with nonstandard growth

Sun-Sig Byun, Hongsoo Kim

We establish interior Lipschitz regularity for solutions to anisotropic fully nonlinear equations with nonstandard growth, without imposing any restriction on the gap between the h…

Calderón-Zygmund estimates for double phase problems with matrix weights

Sun-Sig Byun, Yumi Cho, Seungjin Ryu

We establish an optimal Calderón-Zygmund theory for nonuniformly elliptic double phase problems with matrix weights. For $1 < p < q < \infty$ , $a (\cdot) \in C^{0, α} (Ω)$ ( $0 < α \leq 1$ ), and a…

Lipschitz regularity for fully nonlinear elliptic equations with $(p, q)$ -growth

Sun-Sig Byun, Hongsoo Kim

We prove the interior and global Lipschitz regularity results for a solution of fully nonlinear equations with $(p, q)$ -growth. We prove that for a small gap $q - p$ , a solution is lo…

math.AP2024

Interior $W^{2, δ}$ type estimates for degenerate fully nonlinear elliptic equations with $L^{n}$ data

Sun-Sig Byun, Hongsoo Kim, Jehan Oh

We establish interior $W^{2, δ}$ type estimates for a class of degenerate fully nonlinear elliptic equations with $L^{n}$ data. The main idea of our approach is to slide $C^{1, α}$ con…

math.AP2024

Global Calderón-Zygmund theory for fractional Laplacian type equations

Sun-Sig Byun, Kyeong Bae Kim, Deepak Kumar

We establish several fine boundary regularity results of weak solutions to non-homogeneous $s$ -fractional Laplacian type equations. In particular, we prove sharp Calderón-Zygmund t…

math.AP2024

$C^{1, α}$ regularity for degenerate fully nonlinear elliptic equations with oblique boundary conditions on $C^{1}$ domains

Sun-Sig Byun, Hongsoo Kim, Jehan Oh

We provide a sharp $C^{1, α}$ estimate up to the boundary for a viscosity solution of a degenerate fully nonlinear elliptic equation with the oblique boundary condition on a $C^{1}$ d…

Existence of very weak solutions to nonlinear elliptic equation with nonstandard growth and global weighted gradient estimates

Sun-Sig Byun, Minkyu Lim

We study a general class of quasilinear elliptic equations with nonstandard growth to prove the existence of a very weak solution to such a problem. A key ingredient in the proof i…

Singular elliptic measure data problems with irregular obstacles

Sun-Sig Byun, Kyeong Song, Yeonghun Youn

We investigate elliptic irregular obstacle problems with $p$ -growth involving measure data. Emphasis is on the strongly singular case $1 < p \leq 2 - 1/ n$ , and we obtain several new c…

Calderón-Zygmund theory of nonlocal parabolic equations with discontinuous coefficients

Sun-Sig Byun, Kyeongbae Kim, Deepak Kumar

We prove Calderón-Zygmund type estimates of weak solutions to non-homogeneous nonlocal parabolic equations under a minimal regularity requirement on kernel coefficients. In particu…

Higher Hölder regularity for nonlocal parabolic equations with irregular kernels

Sun-Sig Byun, Hyojin Kim, Kyeongbae Kim

We study a nonlocal parabolic equation with an irregular kernel coefficient to establish higher Hölder regularity under an appropriate higher integrablilty on the nonhomogeneous te…

Regularity results for a class of nonlocal double phase equations with VMO coefficients

Sun-Sig Byun, Kyeongbae Kim, Deepak Kumar

We study a class of nonlocal double phase problems with discontinuous coefficients. A local self-improving property and a higher Hölder continuity result for weak solutions to such…