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January  2009, 8(1): 83-94. doi: 10.3934/cpaa.2009.8.83

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, United States
2. 

University of Bonn, Institut fur Angewandte Mathematik, Germany

Received  March 2008 Revised  August 2008 Published  October 2008

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: Hamiltonians., Nonlinear elliptic and parabolic equations, stochastic differential games.
Mathematics Subject Classification: 35J60, 35K5.
Citation: Alain Bensoussan, Jens Frehse. On diagonal elliptic and parabolic systems with super-quadratic Hamiltonians. Communications on Pure and Applied Analysis, 2009, 8 (1) : 83-94. doi: 10.3934/cpaa.2009.8.83
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