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Smooth Solutions of systemsof quasilinear parabolic equations

Published online by Cambridge University Press:  15 August 2002

Alain Bensoussan  and
Jens Frehse
Alain Bensoussan
Affiliation:
University Paris-Dauphine and CNES, France.
Jens Frehse
Affiliation:
Institut für Angewandte Mathematik der Universität Bonn, Germany.
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Abstract

We consider in this article diagonal parabolic systems arising in the context of stochastic differential games.We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games.Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear Hamiltonian seems to be the adequate one to achieve the regularity property. A key step in the theory is to prove the existence of Hölder solution.

Keywords

Parabolic equationsquasilineargame theoryregularityStochastic optimal controlsmallness conditionspecific structuremaximum principleGreen functionHamiltonian.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 169 - 193
Copyright
© EDP Sciences, SMAI, 2002

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