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

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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 languageEnglish
Pages (from-to)2163-2173
Number of pages11
JournalProceedings of the American Mathematical Society
Volume129
Issue number7
DOIs
Publication statusPublished - 2001

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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