Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds. (English) Zbl 1328.58014
Summary: We derive a priori estimates for second order derivatives of solutions to a wide class of fully nonlinear elliptic equations on Riemannian manifolds. There had been significant work in this direction, especially in connection with important geometric problems and other applications, but one had to make use of the special structures or needed extra assumptions which are more technical in nature to overcome various difficulties. In this paper, we are able to remove most of the technical assumptions and derive the estimates under conditions which are close to optimal. These estimates enable one to prove existence results which are new even for bounded domains in Euclidean space.
MSC:
| 58J05 | Elliptic equations on manifolds, general theory |
| 35J15 | Second-order elliptic equations |
| 35B45 | A priori estimates in context of PDEs |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
Keywords:
a priori estimates; second order derivatives of solutions; nonlinear elliptic equations; Riemannian manifoldsReferences:
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