Sun‐Sig Byun

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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

$C^{1, α}$ 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…

math.AP2023

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…

math.AP2023

$L^{q}$ estimates for nonlocal p-Laplacian type equations with BMO kernel coefficients in divergence form

Sun-Sig Byun, Kyeongbae Kim

We study $s$ -fractional $p$ -Laplacian type equations with discontinuous kernel coefficients in divergence form to establish $W^{s + σ, q}$ estimates for any choice of pairs $(σ, q)$ w…

math.AP2023

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…

math.AP2023

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…

Interior W2,δ type estimates for degenerate fully nonlinear elliptic equations with Ln data

C1,α regularity for degenerate fully nonlinear elliptic equations with oblique boundary conditions on C1 domains

Singular elliptic measure data problems with irregular obstacles

Lq estimates for nonlocal p-Laplacian type equations with BMO kernel coefficients in divergence form

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

Regularity results for mixed local and nonlocal double phase functionals

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

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

$L^{q}$ estimates for nonlocal p-Laplacian type equations with BMO kernel coefficients in divergence form