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Sharp estimates for iterated Green functions

Published online by Cambridge University Press:  12 July 2007

H.-Ch. Grunau  and
G. Sweers
H.-Ch. Grunau
Affiliation:
Institut für Analysis und Numerik, Fakultät für Mathematik, Otto-von-Guericke-Universität, Postfach 4120 D-39016 Magdeburg, Germany
G. Sweers
Affiliation:
Applied Mathematical Analysis, ITS, Delft University of Technology, PO Box 5031, 2600 GA Delft, The Netherlands
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Abstract

Optimal pointwise estimates from above and below are obtained for iterated (poly)harmonic Green functions corresponding to zero Dirichlet boundary conditions. For second-order elliptic operators, these estimates hold true on bounded C1,1 domains. For higher-order elliptic operators we have to restrict ourselves to the polyharmonic operator on balls. We will also consider applications to non-cooperatively coupled elliptic systems and to the lifetime of conditioned Brownian motion.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 1 , February 2002 , pp. 91 - 120
Copyright
Copyright © Royal Society of Edinburgh 2002

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