Logarithmic Schr\"odinger Equations in Infinite Dimensions
We study the logarithmic Schr\"odinger equation with finite range potential on $\mathbb{R}^{\mathbb{Z}^d}$. Through a ground-state representation, we associate and construct a global Gibbs measure and show that it satisfies a logarithmic Sobolev inequality. We find estimates on the solutions in...
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| creator | Read, Larry Zegarlinski, Boguslaw Zhang, Mengchun |
| description | We study the logarithmic Schr\"odinger equation with finite range potential
on $\mathbb{R}^{\mathbb{Z}^d}$. Through a ground-state representation, we
associate and construct a global Gibbs measure and show that it satisfies a
logarithmic Sobolev inequality. We find estimates on the solutions in arbitrary
dimension and prove the existence of weak solutions to the infinite-dimensional
Cauchy problem. |
| doi_str_mv | 10.48550/arxiv.2203.05374 |
| format | Article |
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on $\mathbb{R}^{\mathbb{Z}^d}$. Through a ground-state representation, we
associate and construct a global Gibbs measure and show that it satisfies a
logarithmic Sobolev inequality. We find estimates on the solutions in arbitrary
dimension and prove the existence of weak solutions to the infinite-dimensional
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on $\mathbb{R}^{\mathbb{Z}^d}$. Through a ground-state representation, we
associate and construct a global Gibbs measure and show that it satisfies a
logarithmic Sobolev inequality. We find estimates on the solutions in arbitrary
dimension and prove the existence of weak solutions to the infinite-dimensional
Cauchy problem.</description><subject>Mathematics - Analysis of PDEs</subject><subject>Mathematics - Mathematical Physics</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpjYJA0NNAzsTA1NdBPLKrILNMzMjIw1jMwNTY34WSw8slPTyzKLMnIzUxWCE7OKIpRyk_JzEtPLVJwLSxNLMnMzytWyMxT8MxLy8zLLElVcMnMTc0rBgnzMLCmJeYUp_JCaW4GeTfXEGcPXbAt8QVFmbmJRZXxINviwbYZE1YBAJsVNKQ</recordid><startdate>20220310</startdate><enddate>20220310</enddate><creator>Read, Larry</creator><creator>Zegarlinski, Boguslaw</creator><creator>Zhang, Mengchun</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220310</creationdate><title>Logarithmic Schr\"odinger Equations in Infinite Dimensions</title><author>Read, Larry ; Zegarlinski, Boguslaw ; Zhang, Mengchun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2203_053743</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Analysis of PDEs</topic><topic>Mathematics - Mathematical Physics</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Read, Larry</creatorcontrib><creatorcontrib>Zegarlinski, Boguslaw</creatorcontrib><creatorcontrib>Zhang, Mengchun</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Read, Larry</au><au>Zegarlinski, Boguslaw</au><au>Zhang, Mengchun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Logarithmic Schr\"odinger Equations in Infinite Dimensions</atitle><date>2022-03-10</date><risdate>2022</risdate><abstract>We study the logarithmic Schr\"odinger equation with finite range potential
on $\mathbb{R}^{\mathbb{Z}^d}$. Through a ground-state representation, we
associate and construct a global Gibbs measure and show that it satisfies a
logarithmic Sobolev inequality. We find estimates on the solutions in arbitrary
dimension and prove the existence of weak solutions to the infinite-dimensional
Cauchy problem.</abstract><doi>10.48550/arxiv.2203.05374</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs Mathematics - Mathematical Physics Physics - Mathematical Physics |
| title | Logarithmic Schr\"odinger Equations in Infinite Dimensions |
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