Work

Local regularity for mean-field games in the whole space

Year: 2014

Type: preprint

Abstract: In this paper, we investigate the Sobolev regularity for mean-field games in the whole space $\Rr^d$. This is achieved by combining integrability for the solutions of the Fokker-Planck equation with estimates for the Hamilton-Jacobi equation in Sobolev spaces. To avoid the mathematical challenges posed due to the lack of compactness, we prove an entropy dissipation estimate for the adjoint variable. This, together with the non-linear adjoint method, yields uniform estimates for solutions of the Hamilton-Jacobi equation in $W^{1,p}_{loc}(\Rr^d)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1407.0942

Authors: Gomes, Diogo Aguiar, Pimentel, Edgard Almeida

Institutions: King Abdullah University of Science and Technology, Instituto Nacional de Matemática Pura e Aplicada

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: Conselho Nacional de Desenvolvimento Científico e Tecnológico, King Abdullah University of Science and Technology, Fundação para a Ciência e a Tecnologia

Award: G1332397352

OpenAlex ID: W62854809

Cites: 6

Cited by: 24

Related to: 10