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A priori estimates for the obstacle problem of Hessian type equations on Riemannian manifolds

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  • We are concerned with A priori estimates for the obstacle problem of a wide class of fully nonlinear equations on Riemannian manifolds. We use new techniques introduced by Bo Guan and derive new results for A priori second order estimates of its singular perturbation problem under fairly general conditions. By approximation, the existence of a $C^{1,1}$ viscosity solution is proved.
    Mathematics Subject Classification: Primary: 35B45, 35J60; Secondary: 58J05, 35D40.

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