The ‘‘ergodic limit’’ for a viscous Hamilton−Jacobi equation with Dirichlet conditions

  • Alessio Porretta

    Università di Roma, Italy

Abstract

We study the limit, when tends to , of the solutions of the Dirichlet problem

when and is bounded. In case the limit problem does not have any solution, we prove that has a complete blow-up and its behaviour is described in terms of the corresponding ergodic problem with state constraint conditions. In particular, converges to the ergodic constant and converges to the boundary blow-up solution of the ergodic problem associated to the stochastic optimal control with state constraint.

Cite this article

Alessio Porretta, The ‘‘ergodic limit’’ for a viscous Hamilton−Jacobi equation with Dirichlet conditions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), no. 1, pp. 59–78

DOI 10.4171/RLM/561