一个给定平均曲率方程的Dirichlet问题

IF 0.5 4区数学 Q3 MATHEMATICS Hiroshima Mathematical Journal Pub Date : 2019-08-19 DOI:10.32917/hmj/1607396492

Y. Tsukamoto

{"title":"一个给定平均曲率方程的Dirichlet问题","authors":"Y. Tsukamoto","doi":"10.32917/hmj/1607396492","DOIUrl":null,"url":null,"abstract":"We study a prescribed mean curvature problem where we seek a surface whose mean curvature vector coincides with the normal component of a given vector field. We prove that the problem has a solution near a graphical minimal surface if the prescribed vector field is sufficiently small in a dimensionally sharp Sobolev norm.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"The Dirichlet problem for a prescribed mean curvature equation\",\"authors\":\"Y. Tsukamoto\",\"doi\":\"10.32917/hmj/1607396492\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study a prescribed mean curvature problem where we seek a surface whose mean curvature vector coincides with the normal component of a given vector field. We prove that the problem has a solution near a graphical minimal surface if the prescribed vector field is sufficiently small in a dimensionally sharp Sobolev norm.\",\"PeriodicalId\":55054,\"journal\":{\"name\":\"Hiroshima Mathematical Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2019-08-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Hiroshima Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.32917/hmj/1607396492\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hiroshima Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.32917/hmj/1607396492","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 4

摘要

我们研究了一个规定的平均曲率问题，其中我们寻找一个平均曲率向量与给定向量场的法向分量重合的曲面。我们证明了如果指定的向量场在维数尖锐的Sobolev范数中足够小，则该问题在图形最小曲面附近具有解。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

The Dirichlet problem for a prescribed mean curvature equation

We study a prescribed mean curvature problem where we seek a surface whose mean curvature vector coincides with the normal component of a given vector field. We prove that the problem has a solution near a graphical minimal surface if the prescribed vector field is sufficiently small in a dimensionally sharp Sobolev norm.

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

Hiroshima Mathematical Journal 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Hiroshima Mathematical Journal (HMJ) is a continuation of Journal of Science of the Hiroshima University, Series A, Vol. 1 - 24 (1930 - 1960), and Journal of Science of the Hiroshima University, Series A - I , Vol. 25 - 34 (1961 - 1970). Starting with Volume 4 (1974), each volume of HMJ consists of three numbers annually. This journal publishes original papers in pure and applied mathematics. HMJ is an (electronically) open access journal from Volume 36, Number 1.