The first initial-boundary value problem for a class of fully nonlinear parabolic equations on Riemannian manifolds

Heming Jiao; Zhenan Sui

doi:10.1093/imrn/rnu014

The first initial-boundary value problem for a class of fully nonlinear parabolic equations on Riemannian manifolds

Heming Jiao^*
, Zhenan Sui

^*Corresponding author for this work

School of Mathematics

Ohio State University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, we study the first initial-boundary value problem for a class of fully nonlinear parabolic equations on Riemannian manifolds. The main part of this paper is to derive the a priori estimates for the second-order derivatives of solutions by using a new idea that works under very general structure conditions. As an application, the existence of smooth solutions is proved.

Original language	English
Pages (from-to)	2576-2595
Number of pages	20
Journal	International Mathematics Research Notices
Volume	2015
Issue number	9
DOIs	https://doi.org/10.1093/imrn/rnu014
State	Published - 2015

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abstract = "In this paper, we study the first initial-boundary value problem for a class of fully nonlinear parabolic equations on Riemannian manifolds. The main part of this paper is to derive the a priori estimates for the second-order derivatives of solutions by using a new idea that works under very general structure conditions. As an application, the existence of smooth solutions is proved.",

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AB - In this paper, we study the first initial-boundary value problem for a class of fully nonlinear parabolic equations on Riemannian manifolds. The main part of this paper is to derive the a priori estimates for the second-order derivatives of solutions by using a new idea that works under very general structure conditions. As an application, the existence of smooth solutions is proved.

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M3 - 文章

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The first initial-boundary value problem for a class of fully nonlinear parabolic equations on Riemannian manifolds

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