The obstacle problem for conformal metrics on compact Riemannian manifolds

Abstract

Abstract We prove a priori estimates up to their second order derivatives for solutions to the obstacle problem of curvature equations on Riemannian manifolds (Mn,g) $(M^{n}, g)$ arising from conformal deformation. With the a priori estimates the existence of a C1,1 $C^{1,1} $ solution to the obstacle problem with Dirichlet boundary value is obtained by approximation.

Keywords

• Obstacle problem
• A priori estimates
• Hessian equations
• Viscosity solutions
• Riemannian manifolds