Regularity for fully nonlinear elliptic equations in generalized Orlicz spaces
Analysis of PDEs
2025-12-23 v2
Abstract
In this paper, we establish an optimal global Calder\'{o}n-Zygmund type estimate for the viscosity solution to the Dirichlet boundary problem of fully nonlinear elliptic equations with possibly nonconvex nonlinearities. We prove that the Hessian of the solution is as integrable as the nonhomogeneous term in the setting of a given generalized Orlicz space even when the nonlinearity is asymptotically convex with respect to the Hessian of the solution.
Keywords
Cite
@article{arxiv.2512.16600,
title = {Regularity for fully nonlinear elliptic equations in generalized Orlicz spaces},
author = {Sun-Sig Byun and Jeongmin Han and Mikyoung Lee},
journal= {arXiv preprint arXiv:2512.16600},
year = {2025}
}