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Nash equilibria in N ‐person games with super‐quadratic Hamiltonians
Author(s) -
Ebmeyer Carsten,
Urbano José Miguel,
Vogelgesang Jens
Publication year - 2019
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12188
Subject(s) - mathematics , bounded function , sobolev space , differential game , nash equilibrium , hamiltonian (control theory) , quadratic equation , dirichlet distribution , hamilton–jacobi equation , pure mathematics , hamiltonian system , stochastic differential equation , dirichlet problem , mathematical analysis , mathematical economics , combinatorics , mathematical optimization , geometry , boundary value problem
We consider the Hamilton–Jacobi–Bellman system∂ t u − Δ u = H ( u , ∇ u ) + f for u ∈ R N , 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.