34 citations · 107 across the 46 of their papers we have counts for
48 papers
Structured pre-generation elicitation versus single-shot prompting in AI-assisted enterprise decision-making: a randomised online experiment
William Scott-Jackson
Generative AI speeds, and mostly improves, professional work, but there is concern that users who delegate both the production and the evaluation of an answer may accept weak outpu…
Gradient Estimates Near the Natural Exponent for Very Weak Solutions to -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 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--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--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 , (), and a…
Lipschitz regularity for fully nonlinear elliptic equations with -growth
Sun-Sig Byun, Hongsoo Kim
We prove the interior and global Lipschitz regularity results for a solution of fully nonlinear equations with -growth. We prove that for a small gap , a solution is lo…
Interior type estimates for degenerate fully nonlinear elliptic equations with data
Sun-Sig Byun, Hongsoo Kim, Jehan Oh
We establish interior type estimates for a class of degenerate fully nonlinear elliptic equations with data. The main idea of our approach is to slide con…
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 -fractional Laplacian type equations. In particular, we prove sharp Calderón-Zygmund t…
regularity for degenerate fully nonlinear elliptic equations with oblique boundary conditions on domains
Sun-Sig Byun, Hongsoo Kim, Jehan Oh
We provide a sharp estimate up to the boundary for a viscosity solution of a degenerate fully nonlinear elliptic equation with the oblique boundary condition on a 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 -growth involving measure data. Emphasis is on the strongly singular case , 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…
Regularity results for mixed local and nonlocal double phase functionals
Sun-Sig Byun, Ho-Sik Lee, Kyeong Song
We investigate the De Giorgi-Nash-Moser theory for minimizers of mixed local and nonlocal functionals modeled after \[ v \mapsto \int_{\mathbb{R}^{n}}\int_{\mathbb{R}^{n}}\dfrac{|v…
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…
Self-improving properties of very weak solutions to double phase systems
Sumiya Baasandorj, Sun-Sig Byun, Wontae Kim
We prove the self-improving property of very weak solutions to non-uniformly elliptic problems of double phase type in divergence form under sharp assumptions on the nonlinearity.
Gradient estimates of very weak solutions to general quasilinear elliptic equations
Sun-Sig Byun, Minkyu Lim
We establish a gradient estimate for a very weak solution to a quasilinear elliptic equation with a nonstandard growth condition, which is a natural generalization of the -Lapla…
Global Maximal Regularity for Equations with Degenerate Weights
Anna Kh. Balci, Sun-Sig Byun, Lars Diening +1
In this paper we are concerned with global maximal regularity estimates for elliptic equations with degenerate weights. We consider both the linear case and the non-linear case. We…