Regularity for fully nonlinear elliptic equations in generalized Orlicz spaces

TL;DR

This paper proves optimal regularity estimates for solutions to fully nonlinear elliptic equations within generalized Orlicz spaces, even with nonconvex nonlinearities, extending the understanding of solution regularity in complex functional settings.

Contribution

It establishes the first global Calderón-Zygmund estimates for fully nonlinear elliptic equations in generalized Orlicz spaces with possibly nonconvex nonlinearities.

Findings

Hessian of solutions is integrable as the nonhomogeneous term in generalized Orlicz spaces.

Optimal regularity results hold even when nonlinearities are asymptotically convex.

Extends regularity theory to broader functional frameworks.

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.