Open Access
VOL. 24 | 1990 $H_{\infty}$ functional calculus of second order elliptic partial differntial operators on $L^p$ spaces
Xuan Thinh Duong

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

Proc. Centre Math. Appl., 1990: 91-102 (1990)


Let L be a strongly elliptic partial differential operator of second order, with real coefficients on $L^p(\Omega), 1 \lt p \lt \infty$, with either Dirichlet, or Neumann, or "oblique" boundary conditions. Assume that $\Omega$ is an open, bounded domain with $C^2$ boundary. By adding a oonstant, if necessary, we then establish an $H_\infty$, functional calculus which associates an operator m(L) to each bounded holomorphic function m so that \[ \| m (L) \| \leq M \| m \|\infty \] where M is a constmt independent of m. Under suitable asumptions on L, we can also obtain a similar result in the case of Dirichlet boundary conditions where $\Omega$ is a non-smooth domain.


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

MathSciNet: MR1060114

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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