Regularity for Mean-Field Games Systems with Initial-Initial Boundary Conditions: The Subquadratic Case

Diogo A. Gomes; Edgard A. Pimentel

doi:10.1007/978-3-319-16118-1_15

Regularity for Mean-Field Games Systems with Initial-Initial Boundary Conditions: The Subquadratic Case

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In the present paper, we study forward-forward mean-field games with a power dependence on the measure and subquadratic Hamiltonians. These problems arise in the numerical approximation of stationary mean-field games. We prove the existence of smooth solutions under dimension and growth conditions for the Hamiltonian. To obtain the main result, we combine Sobolev regularity for solutions of the Hamilton-Jacobi equation (using Gagliardo-Nirenberg interpolation) with estimates of polynomial type for solutions of the Fokker-Planck equation.

Original language	English (US)
Title of host publication	CIM Series in Mathematical Sciences
Publisher	Springer Nature
Pages	291-304
Number of pages	14
ISBN (Print)	9783319161174
DOIs	https://doi.org/10.1007/978-3-319-16118-1_15
State	Published - 2015

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KAUST Repository Item: Exported on 2021-04-17

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10.1007/978-3-319-16118-1_15

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title = "Regularity for Mean-Field Games Systems with Initial-Initial Boundary Conditions: The Subquadratic Case",

abstract = "In the present paper, we study forward-forward mean-field games with a power dependence on the measure and subquadratic Hamiltonians. These problems arise in the numerical approximation of stationary mean-field games. We prove the existence of smooth solutions under dimension and growth conditions for the Hamiltonian. To obtain the main result, we combine Sobolev regularity for solutions of the Hamilton-Jacobi equation (using Gagliardo-Nirenberg interpolation) with estimates of polynomial type for solutions of the Fokker-Planck equation.",

author = "Gomes, {Diogo A.} and Pimentel, {Edgard A.}",

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year = "2015",

doi = "10.1007/978-3-319-16118-1_15",

language = "English (US)",

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T1 - Regularity for Mean-Field Games Systems with Initial-Initial Boundary Conditions: The Subquadratic Case

AU - Gomes, Diogo A.

AU - Pimentel, Edgard A.

N1 - KAUST Repository Item: Exported on 2021-04-17

PY - 2015

Y1 - 2015

N2 - In the present paper, we study forward-forward mean-field games with a power dependence on the measure and subquadratic Hamiltonians. These problems arise in the numerical approximation of stationary mean-field games. We prove the existence of smooth solutions under dimension and growth conditions for the Hamiltonian. To obtain the main result, we combine Sobolev regularity for solutions of the Hamilton-Jacobi equation (using Gagliardo-Nirenberg interpolation) with estimates of polynomial type for solutions of the Fokker-Planck equation.

AB - In the present paper, we study forward-forward mean-field games with a power dependence on the measure and subquadratic Hamiltonians. These problems arise in the numerical approximation of stationary mean-field games. We prove the existence of smooth solutions under dimension and growth conditions for the Hamiltonian. To obtain the main result, we combine Sobolev regularity for solutions of the Hamilton-Jacobi equation (using Gagliardo-Nirenberg interpolation) with estimates of polynomial type for solutions of the Fokker-Planck equation.

UR - http://hdl.handle.net/10754/668749

UR - https://link.springer.com/chapter/10.1007%2F978-3-319-16118-1_15

U2 - 10.1007/978-3-319-16118-1_15

DO - 10.1007/978-3-319-16118-1_15

M3 - Conference contribution

SN - 9783319161174

SP - 291

EP - 304

BT - CIM Series in Mathematical Sciences

PB - Springer Nature

ER -

Regularity for Mean-Field Games Systems with Initial-Initial Boundary Conditions: The Subquadratic Case

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