Sharp regularity for a class of degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms

TL;DR

This paper establishes sharp interior $C^{1,eta}$ regularity for viscosity solutions to a class of degenerate or singular fully nonlinear elliptic equations with Hamiltonian terms, using a geometric tangential approach.

Contribution

It provides new regularity results for complex elliptic equations with degenerate/singular and Hamiltonian features, advancing understanding of solution smoothness.

Findings

Established sharp interior $C^{1,eta}$ regularity estimates.

Analyzed the interplay between degeneracy/singularity and Hamiltonian growth.

Developed a geometric tangential method for regularity analysis.

Abstract

We investigate the regularity of the viscosity solutions to a class of degenerate/singular fully nonlinear elliptic equations with Hamiltonian terms. To overcome the difficulty caused by the simultaneous presence of the general degenerate/singular gradient terms and Hamiltonian terms, we analyze the coupled interplay between the degeneracy/singularity law and the growth of Hamiltonian terms and establish lower regularity results. Finally, we obtain sharp interior $C^{1,\alpha}$ regularity estimates via a geometric tangential method.