{"title":"关于与有磁场的薛定谔方程相关的平方和算子","authors":"Antonio Bove, Gregorio Chinni","doi":"10.1007/s10231-024-01434-2","DOIUrl":null,"url":null,"abstract":"<div><p>We study the analytic and Gevrey regularity for a “sum of squares” operator closely connected to the Schrödinger equation with minimal coupling. We however assume that the (magnetic) vector potential has some degree of homogeneity and that the Hörmander bracket condition is satisfied. It is shown that the local analytic/Gevrey regularity of the solution is related to the multiplicities of the zeroes of the Lie bracket of the vector fields.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a sum of squares operator related to the Schrödinger equation with a magnetic field\",\"authors\":\"Antonio Bove, Gregorio Chinni\",\"doi\":\"10.1007/s10231-024-01434-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the analytic and Gevrey regularity for a “sum of squares” operator closely connected to the Schrödinger equation with minimal coupling. We however assume that the (magnetic) vector potential has some degree of homogeneity and that the Hörmander bracket condition is satisfied. It is shown that the local analytic/Gevrey regularity of the solution is related to the multiplicities of the zeroes of the Lie bracket of the vector fields.</p></div>\",\"PeriodicalId\":8265,\"journal\":{\"name\":\"Annali di Matematica Pura ed Applicata\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-03-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali di Matematica Pura ed Applicata\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10231-024-01434-2\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali di Matematica Pura ed Applicata","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10231-024-01434-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On a sum of squares operator related to the Schrödinger equation with a magnetic field
We study the analytic and Gevrey regularity for a “sum of squares” operator closely connected to the Schrödinger equation with minimal coupling. We however assume that the (magnetic) vector potential has some degree of homogeneity and that the Hörmander bracket condition is satisfied. It is shown that the local analytic/Gevrey regularity of the solution is related to the multiplicities of the zeroes of the Lie bracket of the vector fields.
期刊介绍：
This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it).
A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.
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