Mikyoung Lee

activity

20192026

ω

-minimizers of functionals with generalized Orlicz growth

28 citations · 29 across the 10 of their papers we have counts for

collaborators

10 papers

math.AP2026

Lipschitz regularity for orthotropic functionals with general growth

Mikyoung Lee, Jihoon Ok, Bianca Stroffolini

We study the local Lipschitz regularity of local minimizers for a class of degenerate orthotropic functionals with $φ$ -growth, where $φ$ is a general N-function. Unlike standard is…

math.AP2025

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…

math.AP2025

Mean oscillation conditions for nonlinear equation and regularity results

Peter Hästö, Mikyoung Lee, Jihoon Ok

We consider general nonlinear elliptic equations of the form \[ \operatorname{div}\, A(x,Du) = 0 \quad \text{in } Ω, \] where $A : Ω \times R^{n} \to R^{n}$ satisfies a qu…

math.AP2023

Calderón-Zygmund estimates for nonlinear equations of differential forms with BMO coefficients

Mikyoung Lee, Jihoon Ok, Juncheol Pyo

We obtain $L^{q}$ -regularity estimates for weak solutions to $p$ -Laplacian type equations of differential forms. In particular, we prove local Calderón-Zygmund type estimates for equ…

math.AP2023

Weighted Hessian estimates in Orlicz spaces for nondivergence elliptic operators with certain potentials

Mikyoung Lee, Yoonjung Lee

We prove interior weighted Hessian estimates in Orlicz spaces for nondivergence type elliptic equations with a lower order term which involves a nonnegative potential satisfying a…

math.AP2021★ 1 cited

$L^{q}$ -regularity for nonlinear elliptic equations with Schrödinger-type lower order terms

Mikyoung Lee, Jihoon Ok

We consider nonlinear elliptic equations of the $p$ -Laplacian type with lower order terms which involve nonnegative potentials satisfying a reverse Hölder type condition. Then we o…

math.AP2021

Parabolic weighted Sobolev-Poincaré type inequalities

Lars Diening, Mikyoung Lee, Jihoon Ok

We derive weighted Sobolev-Poincaré type inequalities in function spaces concerned with parabolic partial differential equations. We consider general weights depending on both spac…

math.AP2020

Hölder continuity of the minimizer of an obstacle problem with generalized Orlicz growth

Arttu Karppinen, Mikyoung Lee

We prove local $C^{0, α}$ - and $C^{1, α}$ -regularity for the local solution to an obstacle problem with non-standard growth. These results cover as special cases standard, variable e…

math.AP2019

Interior and boundary $W^{1, q}$ -estimates for quasi-linear elliptic equations of Schrödinger type

Mikyoung Lee, Jihoon Ok

We consider nonlinear elliptic equations that are naturally obtained from the elliptic Schrödinger equation $- Δ u + V u = 0$ in the setting of the calculus of variations, and obtain $L^…

math.AP2019★ 28 cited

Hölder continuity of $ω$ -minimizers of functionals with generalized Orlicz growth

Petteri Harjulehto, Peter Hästö, Mikyoung Lee

We show local Hölder continuity of quasiminimizers of functionals with non-standard (Musielak--Orlicz) growth. Compared with previous results, we cover more general minimizing func…