Regularity of solutions to degenerate fully nonlinear elliptic equations with variable exponent

We consider the fully nonlinear equation with variable-exponent double phase type degeneracies [vertical bar Du vertical bar(p(x)) + a(x)vertical bar Du vertical bar(q(x))]F(D(2)u) = f(x). Under some appropriate assumptions, by making use of geometric tangential methods and combing a refined improvement-of-flatness approach with compactness and scaling techniques, we obtain the sharp local C-1,C-alpha regularity of viscosity solutions to such equations.