Radial solutions for fully nonlinear elliptic equations of Monge–Ampère type

Abstract

Abstract First, the symmetry of classical solutions to the Monge–Ampère-type equations is obtained by the moving plane method. Then, the existence and nonexistence of radial solutions in a ball are got from the symmetry results. Finally, the existence and nonexistence of classical solutions to Hessian equations in bounded domains are considered.

Keywords

• Monge–Ampère-type equations
• Hessian equations
• Radial symmetry