Wellposedness of the Master Equation for Mean Field Games with Grushin Type Diffusion
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910407474544640 |
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| author | Jiang, Yiming Wei, Yawei Yang, Yiyun |
| author_facet | Jiang, Yiming Wei, Yawei Yang, Yiyun |
| contents | We study the wellposedness of the master equation for a second-order mean field games with the Grushin type diffusion. In order to do this, we obtain the properties of its solution by investigating a degenerate mean field games system for which there exists an equivalent characterization with the master equation. The crucial points of this paper are to explore some regularities of solutions to two types of linear degenerate partial differential equations and a kind of degenerate linear coupled system so as to derive the existence of solutions to the master equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08192 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wellposedness of the Master Equation for Mean Field Games with Grushin Type Diffusion Jiang, Yiming Wei, Yawei Yang, Yiyun Analysis of PDEs We study the wellposedness of the master equation for a second-order mean field games with the Grushin type diffusion. In order to do this, we obtain the properties of its solution by investigating a degenerate mean field games system for which there exists an equivalent characterization with the master equation. The crucial points of this paper are to explore some regularities of solutions to two types of linear degenerate partial differential equations and a kind of degenerate linear coupled system so as to derive the existence of solutions to the master equation. |
| title | Wellposedness of the Master Equation for Mean Field Games with Grushin Type Diffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.08192 |