Systems of Bellman equations to stochastic differential games with non-compact coupling

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1375-1389
Journal / PublicationDiscrete and Continuous Dynamical Systems
Issue number4
Publication statusPublished - Aug 2010
Externally publishedYes


We consider a class of non-linear partial differential systems like - div (a(x)∇uν) + λuν = Hν(x, Du), with applications for the solution of stochastic differential games with N players, where N is an arbitrary but positive number. The Hamiltonian H of the non-linear system satisfies a quadratic growth condition in Du and contains interactions between the players in the form of non-compact coupling terms ∇ui ∇uj. A L ∩ H 1-estimate and regularity results are shown, mainly in two-dimensional space. The coupling arises from cyclic non-market interaction of the control variables.

Research Area(s)

  • Bellman equation, Hamiltonians, Nonlinear elliptic and parabolic equations, Stochastic differential games, Stochastic games