|
A remark on the Harnack inequality for non-self-adjoint evolution equations
Author(s):
Roger
Chen
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2163-2173.
MSC (2000):
Primary 58G11;
Secondary 53C21, 58G30
Posted:
November 30, 2000
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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.
References:
-
- 1.
- R. Chen, Neumann eigenvalue estimate on a compact Riemannian manifold, Proc. Amer. Math. Soc. 108 (1990), 961-970. MR 90g:58135
- 2.
- S. Y. Cheng, P. Li and S. T. Yau, On the upper estimate of the heat kernel of a complete Riemannian manifold, Amer. J. Math. 103 (1981), 1021-1063. MR 83c:58083
- 3.
- P. Li and S. T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), 153-201. MR 87f:58156
- 4.
- J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577-591. MR 28:2356
- 5.
- J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101-134. MR 28:2357
- 6.
- J. Wang, Global heat kernel estimates, Pacific J. of Math. 178 (1997), 377-398. MR 98g:58168
- 7.
- F. W. Warner, Extension of the Rauch comparison theorem to submanifolds, Trans. Amer. Math. Soc. 122 (1966), 341-356. MR 34:759
- 8.
- S. T. Yau, Harnack inequality for non-self-adjoint evolution equations, Math. Res. Letters 2 (1995), 387-399. MR 96k:58211
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
58G11,
53C21, 58G30
Retrieve articles in all Journals with MSC
(2000):
58G11,
53C21, 58G30
Additional Information:
Roger
Chen
Affiliation:
Department of Mathematics, National Cheng Kung University, Tainan, Taiwan
Email:
rchen@mail.ncku.edu.tw
DOI:
10.1090/S0002-9939-00-05799-3
PII:
S 0002-9939(00)05799-3
Keywords:
Harnack inequality,
evolution equation,
interior rolling R-ball
Received by editor(s):
May 27, 1999
Received by editor(s) in revised form:
November 2, 1999
Posted:
November 30, 2000
Additional Notes:
This research was partially supported by a grant from NSC
Communicated by:
Bennett Chow
Copyright of article:
Copyright
2000,
American Mathematical Society
|
Comments: webmaster@ams.org