Abstract
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) |
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Pages (from-to) | 609-628 |
Number of pages | 20 |
Journal | Journal of the London Mathematical Society |
Volume | 99 |
Issue number | 3 |
DOIs | |
State | Published - Jun 1 2019 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics