KdV 和非 KdV 型三阶算子的卡勒曼估计及其应用

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-06-04 DOI:10.1007/s10231-024-01467-7

Serena Federico

{"title":"KdV 和非 KdV 型三阶算子的卡勒曼估计及其应用","authors":"Serena Federico","doi":"10.1007/s10231-024-01467-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we study a class of variable coefficient third order partial differential operators on <span>\\({\\mathbb {R}}^{n+1}\\)</span>, containing, as a subclass, some variable coefficient operators of KdV-type in any space dimension. For such a class, as well as for the adjoint class, we obtain a Carleman estimate and the local solvability at any point of <span>\\({\\mathbb {R}}^{n+1}\\)</span>. A discussion of possible applications in the context of dispersive equations is provided.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01467-7.pdf","citationCount":"0","resultStr":"{\"title\":\"Carleman estimates for third order operators of KdV and non KdV-type and applications\",\"authors\":\"Serena Federico\",\"doi\":\"10.1007/s10231-024-01467-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we study a class of variable coefficient third order partial differential operators on <span>\\\\({\\\\mathbb {R}}^{n+1}\\\\)</span>, containing, as a subclass, some variable coefficient operators of KdV-type in any space dimension. For such a class, as well as for the adjoint class, we obtain a Carleman estimate and the local solvability at any point of <span>\\\\({\\\\mathbb {R}}^{n+1}\\\\)</span>. A discussion of possible applications in the context of dispersive equations is provided.</p></div>\",\"PeriodicalId\":8265,\"journal\":{\"name\":\"Annali di Matematica Pura ed Applicata\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10231-024-01467-7.pdf\",\"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/s10231-024-01467-7\",\"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/s10231-024-01467-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究的是\({\mathbb {R}}^{n+1}\) 上的一类可变系数三阶偏微分算子，其子类包含在任意空间维度上的一些 KdV 型可变系数算子。对于这样的类以及邻接类，我们得到了卡勒曼估计和在\({\mathbb {R}}^{n+1}\) 任意点的局部可解性。我们还讨论了在分散方程中的可能应用。

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

Carleman estimates for third order operators of KdV and non KdV-type and applications

In this paper we study a class of variable coefficient third order partial differential operators on \({\mathbb {R}}^{n+1}\), containing, as a subclass, some variable coefficient operators of KdV-type in any space dimension. For such a class, as well as for the adjoint class, we obtain a Carleman estimate and the local solvability at any point of \({\mathbb {R}}^{n+1}\). A discussion of possible applications in the context of dispersive equations is provided.

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

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

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.