The Logarithmic Gradient of the Kernel of the Heat Equation with Drift on a Riemannian Manifold

J. Bernatska

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The Logarithmic Gradient of the Kernel of the Heat Equation with Drift on a Riemannian Manifold

机译：黎曼流形上带漂移的热方程核的对数梯度

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摘要

For a parabolic equation with drift on a Riemannian manifold of positive curvature we obtain a representation for the logarithmic gradient in the form of the sum of two vector fields one of which is known and the other is bounded. The drift field is assumed to be of sufficiently rapid decay at infinity.

机译：对于在正曲率的黎曼流形上具有漂移的抛物线方程，我们以两个向量场之和的形式获得对数梯度的表示形式，其中一个是已知的，另一个是有界的。假定漂移场在无穷远处具有足够快的衰减。

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《Siberian Mathematical Journal》 |2004年第1期|共8页
作者
J. Bernatska;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
fundamental solution; Riemannian manifold; Laplace–Beltrami operator; vector field;

机译：基本解;黎曼流形;Laplace-Beltrami算子;矢量场;

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专利

1. The Logarithmic Gradient of the Kernel of the Heat Equation with Drift on a Riemannian Manifold [J] . J. Bernatska Siberian Mathematical Journal . 2004,第1期

机译：黎曼流形上带漂移的热方程核的对数梯度
2. SHARP GRADIENT ESTIMATES FOR A HEAT EQUATION IN RIEMANNIAN MANIFOLDS [J] . Ha Tuan Dung, Nguyen Thac Dung Proceedings of the American Mathematical Society . 2019,第12期

机译：黎曼歧管中热方程的尖锐梯度估计
3. Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds [J] . Nguyen Ngoc Khanh Archivum Mathematicum . 2016,第4期

机译：黎曼流形上一般热方程的Li Yau型梯度估计。
4. Smolyanov surface measures and solutions of Schroedinger and heat type equations on a Riemannian manifold [C] . Ya. A. Butko International Confernce on Days on Diffraction . 2006

机译：斯克罗登·歧管施罗德格和热型方程的Smolyanov地表测量和解决方案
5. Heat equations on Lie groups, symmetric spaces and Riemannian manifolds. [D] . Kim, Jinman. 2005

机译：李群，对称空间和黎曼流形上的热方程。
6. SINGULAR INTEGRAL EQUATIONS FOR DIFFERENTIAL FORMS ON RIEMANNIAN MANIFOLDS [O] . J. J. Kohn 1956

机译：Rimannian流形上微分形式的奇异积分方程
7. Gradient estimate for the heat kernel of a complete Riemannian manifold and its applications [O] . Jiayu Li 1991

机译：完整黎曼流形热核的梯度估计及其应用
8. The Conservation Property of the Heat Equation on Riemannian Manifolds [R] . Matthew P. Gaffney 1958

机译：黎曼流形上热方程的守恒性

The Logarithmic Gradient of the Kernel of the Heat Equation with Drift on a Riemannian Manifold

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