Nash equilibria in N-person games with super-quadratic Hamiltonians

Carsten Ebmeyer; José Miguel Urbano; Jens Vogelgesang

doi:10.1112/jlms.12188

Nash equilibria in N-person games with super-quadratic Hamiltonians

Carsten Ebmeyer, José Miguel Urbano, Jens Vogelgesang

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	609-628
Number of pages	20
Journal	Journal of the London Mathematical Society
Volume	99
Issue number	3
DOIs	https://doi.org/10.1112/jlms.12188
State	Published - Jun 1 2019
Externally published	Yes

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Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

General Mathematics

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10.1112/jlms.12188

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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.",

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AU - Vogelgesang, Jens

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PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

AB - 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.

UR - https://onlinelibrary.wiley.com/doi/abs/10.1112/jlms.12188

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M3 - Article

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JF - Journal of the London Mathematical Society

IS - 3

ER -

Nash equilibria in N-person games with super-quadratic Hamiltonians

Abstract

Bibliographical note

ASJC Scopus subject areas

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