海森堡周期情况下的连续性方程：表示公式及平均场博弈的应用

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-07-11 DOI:10.1007/s00030-024-00967-y

Alessandra Cutrì, Paola Mannucci, Claudio Marchi, Nicoletta Tchou

{"title":"海森堡周期情况下的连续性方程：表示公式及平均场博弈的应用","authors":"Alessandra Cutrì, Paola Mannucci, Claudio Marchi, Nicoletta Tchou","doi":"10.1007/s00030-024-00967-y","DOIUrl":null,"url":null,"abstract":"We provide a representation of the weak solution of the continuity equation on the Heisenberg group \\({\\mathbb {H}}^1\\) with periodic data (the periodicity is suitably adapted to the group law). This solution is the push forward of a measure concentrated on the flux associated with the drift of the continuity equation. Furthermore, we shall use this interpretation for proving that weak solutions to first order Mean Field Games on \\({\\mathbb {H}}^1\\) are also mild solutions.\n","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"36 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The continuity equation in the Heisenberg-periodic case: a representation formula and an application to Mean Field Games\",\"authors\":\"Alessandra Cutrì, Paola Mannucci, Claudio Marchi, Nicoletta Tchou\",\"doi\":\"10.1007/s00030-024-00967-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We provide a representation of the weak solution of the continuity equation on the Heisenberg group \\\\({\\\\mathbb {H}}^1\\\\) with periodic data (the periodicity is suitably adapted to the group law). This solution is the push forward of a measure concentrated on the flux associated with the drift of the continuity equation. Furthermore, we shall use this interpretation for proving that weak solutions to first order Mean Field Games on \\\\({\\\\mathbb {H}}^1\\\\) are also mild solutions.\\n\",\"PeriodicalId\":501665,\"journal\":{\"name\":\"Nonlinear Differential Equations and Applications (NoDEA)\",\"volume\":\"36 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Differential Equations and Applications (NoDEA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00030-024-00967-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Differential Equations and Applications (NoDEA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00030-024-00967-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们提供了海森堡群 \({\mathbb {H}}^1\)上连续性方程弱解的周期性数据表示（周期性是根据群法适当调整的）。这种解是对与连续性方程漂移相关的通量集中的度量的推进。此外，我们将用这种解释来证明一阶平均场博弈在 \({\mathbb {H}}^1\) 上的弱解也是温和解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The continuity equation in the Heisenberg-periodic case: a representation formula and an application to Mean Field Games

We provide a representation of the weak solution of the continuity equation on the Heisenberg group \({\mathbb {H}}^1\) with periodic data (the periodicity is suitably adapted to the group law). This solution is the push forward of a measure concentrated on the flux associated with the drift of the continuity equation. Furthermore, we shall use this interpretation for proving that weak solutions to first order Mean Field Games on \({\mathbb {H}}^1\) are also mild solutions.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Nonlinear Differential Equations and Applications (NoDEA)

自引率

0.00%

发文量