We consider the Hamilton–Jacobi–Bellman system (Formula presented.) for u E RN, where the Hamiltonian H(u,∇u) satisfies a super-quadratic growth condition with respect to |∇u|. Such a non-linear parabolic system corresponds to a stochastic differential game with N players. We obtain the existence of bounded weak solutions and prove regularity results in Sobolev spaces for the Dirichlet problem.
|Original language||English (US)|
|Number of pages||20|
|Journal||Journal of the London Mathematical Society|
|State||Published - Jun 1 2019|
Bibliographical noteGenerated from Scopus record by KAUST IRTS on 2023-02-15
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