{"title":"非局部Hamilton-Jacobi-Bellman方程周期均匀化的收敛速率","authors":"Andrei Rodríguez-Paredes, Erwin Topp","doi":"10.1051/cocv/2023038","DOIUrl":null,"url":null,"abstract":"In this paper we provide a rate of convergence for periodic homogenization of Hamilton–Jacobi–Bellman equations with nonlocal diffusion. The result is based on the regularity of the associated effective problem, where convexity plays a crucial role. The necessary regularity estimates are made possible by a representation formula we obtain for the effective Hamiltonian, a result that has an independent interest.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rates of convergence in periodic homogenization of nonlocal Hamilton–Jacobi–Bellman equations,\",\"authors\":\"Andrei Rodríguez-Paredes, Erwin Topp\",\"doi\":\"10.1051/cocv/2023038\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we provide a rate of convergence for periodic homogenization of Hamilton–Jacobi–Bellman equations with nonlocal diffusion. The result is based on the regularity of the associated effective problem, where convexity plays a crucial role. The necessary regularity estimates are made possible by a representation formula we obtain for the effective Hamiltonian, a result that has an independent interest.\",\"PeriodicalId\":50500,\"journal\":{\"name\":\"Esaim-Control Optimisation and Calculus of Variations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Control Optimisation and Calculus of Variations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/cocv/2023038\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Control Optimisation and Calculus of Variations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/cocv/2023038","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Rates of convergence in periodic homogenization of nonlocal Hamilton–Jacobi–Bellman equations,
In this paper we provide a rate of convergence for periodic homogenization of Hamilton–Jacobi–Bellman equations with nonlocal diffusion. The result is based on the regularity of the associated effective problem, where convexity plays a crucial role. The necessary regularity estimates are made possible by a representation formula we obtain for the effective Hamiltonian, a result that has an independent interest.
期刊介绍:
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in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.