Interior regularity estimates for fully nonlinear equations with arbitrary nonhomogeneous degeneracy laws

Abstract: In this paper, we study regularity estimates for a class of degenerate, fully nonlinear elliptic equations with arbitrary nonhomogeneous degeneracy laws. We establish that viscosity solutions are locally continuously differentiable under suitable conditions on the degeneracy laws. Our proof employs improvement of flatness techniques alongside an alternative recursive algorithm for renormalizing the approximating solutions, linking our model to the homogeneous, fully nonlinear, uniformly elliptic equation.