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Équations elliptiques non linéaires avec conditions aux limites infinies et contrôle stochastique avec constraintes d’état. (Nonlinear elliptic equations with infinite boundary conditions and stochastic control with state constraints). (French) Zbl 0568.35042

The main results are the existence and the uniqueness of solutions of nonlinear elliptic equations which blow up at the boundary. This infinite boundary condition corresponds to a stochastic control problem with state constraints. A particular case is treated as an illustrative example: \[ - \Delta u+m| \nabla u|^ p+\lambda u=f\quad in\quad \Omega,\quad u\in C^ 2(\Omega),\quad u(x)\to \infty \quad as\quad d(x,\partial \Omega)\to 0. \]
Reviewer: S.M.Lenhart

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
93E20 Optimal stochastic control
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
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