Smooth Solutions of systems of quasilinear parabolic equations
and CNES, France.
2 Institut für Angewandte Mathematik der Universität Bonn, Germany.
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.
Mathematics Subject Classification: 35XX / 49XX
Key words: Parabolic equations / quasilinear / game theory / regularity / Stochastic optimal control / smallness condition / specific structure / maximum principle / Green function / Hamiltonian.
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