Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method
We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from $L^p$-rates of convergence for the vanishing viscosity approximation to regularizing effects for the Cauchy problem in the whole Euclidean space and Liouville-type theo...
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| creator | Camilli, Fabio Goffi, Alessandro Mendico, Cristian |
| description | We provide some new integral estimates for solutions to Hamilton-Jacobi
equations and we discuss several consequences, ranging from $L^p$-rates of
convergence for the vanishing viscosity approximation to regularizing effects
for the Cauchy problem in the whole Euclidean space and Liouville-type
theorems. Our approach is based on duality techniques \`a la Evans and a
careful study of advection-diffusion equations. The optimality of the results
is discussed by several examples. |
| doi_str_mv | 10.48550/arxiv.2307.12932 |
| format | Article |
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equations and we discuss several consequences, ranging from $L^p$-rates of
convergence for the vanishing viscosity approximation to regularizing effects
for the Cauchy problem in the whole Euclidean space and Liouville-type
theorems. Our approach is based on duality techniques \`a la Evans and a
careful study of advection-diffusion equations. The optimality of the results
is discussed by several examples.</description><identifier>DOI: 10.48550/arxiv.2307.12932</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2023-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2307.12932$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2307.12932$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Camilli, Fabio</creatorcontrib><creatorcontrib>Goffi, Alessandro</creatorcontrib><creatorcontrib>Mendico, Cristian</creatorcontrib><title>Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method</title><description>We provide some new integral estimates for solutions to Hamilton-Jacobi
equations and we discuss several consequences, ranging from $L^p$-rates of
convergence for the vanishing viscosity approximation to regularizing effects
for the Cauchy problem in the whole Euclidean space and Liouville-type
theorems. Our approach is based on duality techniques \`a la Evans and a
careful study of advection-diffusion equations. The optimality of the results
is discussed by several examples.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNo1z71OwzAYhWEvDKhwAUz4BhKcz00cj1UpFFQJkLpHn_9UV4kdHDeCu0cUOh29y5EeQu4qVi7bumYPmL78XAJnoqxAcrgm-HHCkH3G7GdLMRj6ecL-0mOKo03Z24m6mOgWB9_nGIpX1FF5-v64mejskeaDpSGG3geLiaI5Rh8yHWw-RHNDrhz2k7393wXZP232622xe3t-Wa92BTYCCs0bo5UDaRtEBuCYrRxoIaBtNC6lVMJoU_MaNLgWuamMFEo5xTRwx4AvyP3f7dnYjckPmL67X2t3tvIfAdFRQA</recordid><startdate>20230724</startdate><enddate>20230724</enddate><creator>Camilli, Fabio</creator><creator>Goffi, Alessandro</creator><creator>Mendico, Cristian</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230724</creationdate><title>Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method</title><author>Camilli, Fabio ; Goffi, Alessandro ; Mendico, Cristian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-c36dcbf29e6aa022f0e1f2c77286ca499b7dcd5352c2f8a3d1d97bbfb0c23f023</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Camilli, Fabio</creatorcontrib><creatorcontrib>Goffi, Alessandro</creatorcontrib><creatorcontrib>Mendico, Cristian</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Camilli, Fabio</au><au>Goffi, Alessandro</au><au>Mendico, Cristian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method</atitle><date>2023-07-24</date><risdate>2023</risdate><abstract>We provide some new integral estimates for solutions to Hamilton-Jacobi
equations and we discuss several consequences, ranging from $L^p$-rates of
convergence for the vanishing viscosity approximation to regularizing effects
for the Cauchy problem in the whole Euclidean space and Liouville-type
theorems. Our approach is based on duality techniques \`a la Evans and a
careful study of advection-diffusion equations. The optimality of the results
is discussed by several examples.</abstract><doi>10.48550/arxiv.2307.12932</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method |
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