### Abstract

In this paper we consider a non-self-adjoint evolution equation on a compact Riemannian manifold with boundary. We prove a Harnack inequality for a positive solution satisfying the Neumann boundary condition. In particular, the boundary of the manifold may be nonconvex and this gives a generalization to a theorem of Yau.

Original language | English |
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Pages (from-to) | 2163-2173 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 129 |

Issue number | 7 |

Publication status | Published - 2001 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Proceedings of the American Mathematical Society*, vol. 129, no. 7, pp. 2163-2173.

**A remark on the harnack inequality for non-self-adjoint evolution equations.** / Chen, Roger R.-C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A remark on the harnack inequality for non-self-adjoint evolution equations

AU - Chen, Roger R.-C.

PY - 2001

Y1 - 2001

N2 - In this paper we consider a non-self-adjoint evolution equation on a compact Riemannian manifold with boundary. We prove a Harnack inequality for a positive solution satisfying the Neumann boundary condition. In particular, the boundary of the manifold may be nonconvex and this gives a generalization to a theorem of Yau.

AB - In this paper we consider a non-self-adjoint evolution equation on a compact Riemannian manifold with boundary. We prove a Harnack inequality for a positive solution satisfying the Neumann boundary condition. In particular, the boundary of the manifold may be nonconvex and this gives a generalization to a theorem of Yau.

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UR - http://www.scopus.com/inward/citedby.url?scp=23044529564&partnerID=8YFLogxK

M3 - Article

VL - 129

SP - 2163

EP - 2173

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 7

ER -