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arXiv · 2512.16600

Regularity for fully nonlinear elliptic equations in generalized Orlicz spaces

Sun-Sig Byun·Jeongmin Han·Mikyoung Lee
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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.

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Sun-Sig Byun, Jeongmin Han, Mikyoung Lee. 2025-12-18. Regularity for fully nonlinear elliptic equations in generalized Orlicz spaces. https://arxiv.org/abs/2512.16600

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