Higher H\"{o}lder regularity for degenerate fully nonlinear elliptic equations with Hamiltonian terms
This paper focuses on a class of fully nonlinear elliptic equations with variable double phase type degeneracy law and Hamiltonian terms. We obtain improved gradient H\"{o}lder regularity results at points where the Hamiltonian coefficients and source terms vanish. Furthermore, we establish a Schauder-type estimate at local extrema, which is sharp with respect to the vanishing rate of the Hamiltonian coefficient and source term. Our approach adapts compactness and dichotomy arguments to capture the interplay between the degeneracy rate and the growth of the Hamiltonian term.
math.AP↗