Regularity for fully nonlinear elliptic equations in generalized Orlicz spaces

2025/12/18 by Byun, Sun-Sig, Han, Jeongmin, Lee, Mikyoung
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.16600

Abstract

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 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.

Citations

• Sharp hessian integrability estimates for nonlinear elliptic equations:\n an asymptotic approach
• On the existence of W²_p solutions for fully nonlinear elliptic equations under relaxed convexity assumptions

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• Sharp boundary and global regularity for degenerate fully nonlinear elliptic equations
• Global regularity results for a class of singular/degenerate fully nonlinear elliptic equations
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• Global Calderón-Zygmund estimates for asymptotically convex fully nonlinear Grad-Mercier type equations