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VOL. 24 | 1990 The uniqueness of diffusion semigroups
Brian Jefferies

Editor(s) Ian Doust, Brian Jefferies, Alan McIntosh


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 $x \in \mathbb(R)^d$.


Published: 1 January 1990
First available in Project Euclid: 18 November 2014

zbMATH: 0704.60078
MathSciNet: MR1060118

Rights: Copyright © 1990, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.


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