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On a $\nu$-continuous family of strong solutions to the Euler or Navier-Stokes equations with the Navier-Type boundary condition
Systems of Bellman equations to stochastic differential games with non-compact coupling
| 1. | School of Management, International Center for Decision and Risk Analysis, University of Texas at Dallas, 800 W. Campbell Rd, SM30, Richardson, TX 75080-3021, United States |
| 2. | Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, NRW, 53115 Bonn, Germany |
| 3. | Harvard Mathematics Department, One Oxford Street, Cambridge, MA 02138, United States |
-div$(a(x)\nabla u_{\nu}) +\lambda u_{\nu}=H_{\nu}(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 $D u$ and contains interactions between the players in the form of non-compact coupling terms $\nabla u_{i} \cdot\nabla u_j$. A $L^{\infty}\cap H^1$-estimate and regularity results are shown, mainly in two-dimensional space. The coupling arises from cyclic non-market interaction of the control variables.
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