On diagonal elliptic and parabolic systems withsuper-quadratic Hamiltonians

Alain Bensoussan; Jens Frehse

doi:10.3934/cpaa.2009.8.83

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2009, Volume 8, Issue 1: 83-94. Doi: 10.3934/cpaa.2009.8.83

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On diagonal elliptic and parabolic systems with super-quadratic Hamiltonians

Alain Bensoussan^1, and
Jens Frehse^2,

1.
University of Texas at Dallas, School of Management, International Center for Decision and Risk Analysis
2.
University of Bonn, Institut fur Angewandte Mathematik

Received: February 29, 2008

Revised: July 31, 2008

Published: December 2008

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Abstract

We consider in this article a class of systems of second order partial differential equations with non-linearity in the first order derivative and zero order term which can be super-quadratic. These problems are motivated by differential geometry and stochastic differential games. Up to now, in the case of systems, only quadratic growth had been considered.

Keywords:

Nonlinear elliptic and parabolic equations,
stochastic differential games,
Hamiltonians.

Mathematics Subject Classification: 35J60, 35K55.

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