Vol. 8, No. 5, 2015

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On estimates for fully nonlinear parabolic equations on Riemannian manifolds

Bo Guan, Shujun Shi and Zhenan Sui

Vol. 8 (2015), No. 5, 1145–1164
Abstract

We present some new ideas to derive a priori second-order estimates for a wide class of fully nonlinear parabolic equations. Our methods, which produce new existence results for the initial-boundary value problems in n, are powerful enough to work in general Riemannian manifolds.

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Keywords
fully nonlinear parabolic equations, a priori estimates, subsolutions, concavity
Mathematical Subject Classification 2010
Primary: 35K55
Secondary: 35B45, 58J35
Milestones
Received: 21 October 2014
Revised: 13 February 2015
Accepted: 30 April 2015
Published: 28 July 2015
Authors
Bo Guan
Department of Mathematics
Ohio State University
231 W 18th Street
Columbus, OH 43210
United States
School of Mathematical Sciences
Xiamen University
Xiamen 361005
China
Shujun Shi
School of Mathematical Sciences
Harbin Normal University
Harbin 150025
China
Zhenan Sui
Department of Mathematics
Ohio State University
231 W 18th Street
Columbus, OH 43210
United States