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VOL. 57 | 2010 Non-symmetric diffusions on a Riemannian manifold
Ichiro Shigekawa

Editor(s) Motoko Kotani, Masanori Hino, Takashi Kumagai

## Abstract

We consider a non-symmetric diffusion on a Riemannian manifold generated by $\mathfrak{A} = \frac{1}{2}\triangle + b$. We give a sufficient condition for which $\mathfrak{A}$ generates a $C_0$-semigroup in $L^2$. To do this, we show that $\mathfrak{A}$ is maximal dissipative. Further we give a characterization of the generator domain.

We also discuss the same issue in $L^p$ ($1 \lt p \lt \infty$) setting and give a sufficient condition for which $\mathfrak{A}$ generates a $C_0$-semigroup in $L^p$.

## Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1200.58024
MathSciNet: MR2648272

Digital Object Identifier: 10.2969/aspm/05710437

Subjects:
Primary: 35P15 , 58J65 , 60J60

Keywords: generator domain , maximal dissipative operator , Non-symmetric diffusion , Riemannian manifold