On diagonal elliptic and parabolic systems with super-quadratic Hamiltonians

Pages: 83 - 94, Volume 8, Issue 1, January 2009

doi:10.3934/cpaa.2009.8.83       Abstract        Full Text (173.4K)       Related Articles

Alain Bensoussan - University of Texas at Dallas, School of Management, International Center for Decision and Risk Analysis, United States (email)
Jens Frehse - University of Bonn, Institut fur Angewandte Mathematik, Germany (email)

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.

Received: March 2008;      Revised: August 2008;      Published: October 2008.