## Advanced Studies in Pure Mathematics

### Non-symmetric diffusions on a Riemannian manifold

Ichiro Shigekawa

#### 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 $L^p$.

#### Article information

Dates
Revised: 17 July 2009
First available in Project Euclid: 24 November 2018

https://projecteuclid.org/ euclid.aspm/1543086331

Digital Object Identifier
doi:10.2969/aspm/05710437

Mathematical Reviews number (MathSciNet)
MR2648272

Zentralblatt MATH identifier
1200.58024

#### Citation

Shigekawa, Ichiro. Non-symmetric diffusions on a Riemannian manifold. Probabilistic Approach to Geometry, 437--461, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710437. https://projecteuclid.org/euclid.aspm/1543086331