Improved regularity estimates for degenerate/singular fully nonlinear systems and Hardy-Hénon-type equations

Abstract: In this paper, we study the degenerate/singular fully nonlinear dead-core systems coupled with strong absorption terms. Several properties, such as improved regularity for viscosity solutions along the free boundary, non-degeneracy, a measure estimate of free boundary, some Liouville-type results, and the behavior of blow-up solution, are proved. We also investigate sharp and improved regularity estimates for viscosity solutions to Hardy-H\'{e}non-type equations with possibly singular weight and strong absorption ruled by degenerate/singular fully nonlinear operator. Our findings are new even for the model equations, involving a degenerate/singular Laplacian operator.