Proceedings of the Centre for Mathematics and its Applications

The uniqueness of diffusion semigroups

Brian Jefferies

Full-text: Open access

Abstract

It is shown that if the highest order co-efficients of a uniformly elliptic second order differential operator $L$ on $\mathbb{R}^d$ are bounded and Hölder continuous, and the other coefficients are bounded and measurable, then there is at most one semigroup $S$ acting on bounded Borel measurable functions, such that $S$ is given by a transition function, and for all smooth functons $f$ with compact support in $\mathbb{R}^d, S(t)f(x) + \int_0^t S(s)Lf(x) ds$ for all $t > 0$ and $x \in \mathbb(R)^d$.

Article information

Source
Miniconference on Operators in Analysis. Ian Doust, Brian Jefferies, Chun Li, and Alan McIntosh, eds. Proceedings of the Centre for Mathematical Analysis, v. 24. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1990), 126-134

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416335067

Mathematical Reviews number (MathSciNet)
MR1060118

Zentralblatt MATH identifier
0704.60078

Citation

Jefferies, Brian. The uniqueness of diffusion semigroups. Miniconference on Operators in Analysis, 126--134, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1990. https://projecteuclid.org/euclid.pcma/1416335067


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