10 papers
Gradient continuity for -Laplacian obstacle problems under mean oscillation conditions
Sungjin Lee, Jihoon Ok
We establish the -regularity of solutions to the obstacle problems associated with -Laplacian type equations, where . Specifically, we prove that the gradient o…
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 -growth, where is a general N-function. Unlike standard…
Wolff potentials and nonlocal equations of Lane-Emden type
Quoc-Hung Nguyen, Jihoon Ok, Kyeong Song
We consider nonlocal equations of the type \[ (-Î_{p})^{s}u = μ\quad \text{in}\;\; Ω, \] where is either a bounded domain or the whole $\mathbb{R}^{n}…
Higher integrability for parabolic PDEs with generalized Orlicz growth
Peter Hästö, Jihoon Ok
We prove higher integrability of the gradient of weak solutions to nonlinear parabolic systems whose prototype is \[ \partial_t u-\mathrm{div}\Big(\frac{Ï'(z, |\nabla u|)}{|\nabla…
Double phase quasiconvex functionals and their partial regularity theory
Sunwoo Jeong, Jihoon Ok
We consider degenerate nonautonomous energies for vector-valued functions , where the integrand satisfies grow…
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 satisfies a…