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The first initial-boundary value problem for Hessian equations of parabolic type on Riemannian manifolds. (English) Zbl 1382.35145

Summary: In this paper, we are concerned with the first initial-boundary value problem for a class of fully nonlinear parabolic equations on Riemannian manifolds. As usual, the establishment of the a priori \(C^2\) estimates is our main part. Based on these estimates, the existence of classical solutions is proved under conditions which are nearly optimal.

MSC:

35K96 Parabolic Monge-Ampère equations
35B45 A priori estimates in context of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35R01 PDEs on manifolds
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