# Smooth solutions of systems of quasilinear parabolic equations

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- Volume: 8, page 169-193
- ISSN: 1292-8119

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topBensoussan, Alain, and Frehse, Jens. "Smooth solutions of systems of quasilinear parabolic equations." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 169-193. <http://eudml.org/doc/245506>.

@article{Bensoussan2002,

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.},

author = {Bensoussan, Alain, Frehse, Jens},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {parabolic equations; quasilinear; game theory; regularity; stochastic optimal control; smallness condition; specific structure; maximum principle; Green function; hamiltonian; quadratic nonlinearity},

language = {eng},

pages = {169-193},

publisher = {EDP-Sciences},

title = {Smooth solutions of systems of quasilinear parabolic equations},

url = {http://eudml.org/doc/245506},

volume = {8},

year = {2002},

}

TY - JOUR

AU - Bensoussan, Alain

AU - Frehse, Jens

TI - Smooth solutions of systems of quasilinear parabolic equations

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

PB - EDP-Sciences

VL - 8

SP - 169

EP - 193

AB - 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.

LA - eng

KW - parabolic equations; quasilinear; game theory; regularity; stochastic optimal control; smallness condition; specific structure; maximum principle; Green function; hamiltonian; quadratic nonlinearity

UR - http://eudml.org/doc/245506

ER -

## References

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