On the mean field games system with lateral Cauchy data via Carleman estimates-Reference-Cited by-同舟云学术

On the mean field games system with lateral Cauchy data via Carleman estimates

Published:2024-02-01 Issue:2 Volume:32 Page:277-295
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Klibanov Michael V.¹,Li Jingzhi²,Liu Hongyu³

Affiliation:

1. Department of Mathematics and Statistics , University of North Carolina at Charlotte , Charlotte , NC, 28223 , USA

2. Department of Mathematics & National Center for Applied Mathematics Shenzhen & SUSTech International Center for Mathematics , Southern University of Science and Technology , Shenzhen 518055 , P. R. China

3. Department of Mathematics , City University of Hong Kong , Kowloon , Hong Kong SAR , P. R. China

Abstract

Abstract The second-order mean field games system (MFGS) in a bounded domain with the lateral Cauchy data are considered. This means that both Dirichlet and Neumann boundary data for the solution of the MFGS are given. Two Hölder stability estimates for two slightly different cases are derived. These estimates indicate how stable the solution of the MFGS is with respect to the possible noise in the lateral Cauchy data. Our stability estimates imply uniqueness. The key mathematical apparatus is the apparatus of two new Carleman estimates.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Guangdong Province

Shenzhen Scientific and Technological Foundation

Research Grants Council, University Grants Committee

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2023-0089/pdf

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