Year: 1986
Type: article
Abstract: In this paper, we will study parabolic equations of the typeon a general Riemannian manifold.The function q(x, t) is assumed to be C 2 in the first variable and C 1 in the second variable.In classical situations [20], a Harnack inequality for positive solutions was established locally.However, the geometric dependency of the estimates is complicated and sometimes unclear.Our goal is to prove a Harnack inequality for positive solutions of (0.1) (w 2) by utilizing a gradient estimate derived in w 1.The method of proof is originated in [26] and [8], where they have studied the elliptic case, i.e. the solution is time independent.In some situations (Theorems 2.2 and
Source: Acta Mathematica
DOI: 10.1007/bf02399203
Authors: Peter Li, Shing Tung Yau
Institutions: University of Utah, University of California San Diego
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W1970224775