## Ohio State University Partial Differential Equations Seminar## Year 2018-2019Time/Location: Wednesdays 11:00 am- noon / MW 154 (unless otherwise noted) |
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Abstract: Fully nonlinear partial differential equations play important roles in geo- metric problems, such as curvature equations in classical geometry and the Yamabe problems on manifolds. A key to understand these equations is to establish a priori estimates for these equations. The Dirichlet problems have received much attention. In this talk we report some recent results joint with Professor Guan Bo for the Neu- mann problem of fully nonlinear elliptic equations on Riemannian manifolds. We try to delete the structural condition for the Neumann boundary in deriving estimates for second derivatives. And we use a priori estimates and blow-up methods to derive the gradient estimates.

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