多个开放弧线上边界积分算子的形状全貌

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-27 DOI:10.1007/s00041-024-10071-5

José Pinto, Fernando Henríquez, Carlos Jerez-Hanckes

{"title":"多个开放弧线上边界积分算子的形状全貌","authors":"José Pinto, Fernando Henríquez, Carlos Jerez-Hanckes","doi":"10.1007/s00041-024-10071-5","DOIUrl":null,"url":null,"abstract":"<p>We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting the corresponding boundary value problems as boundary integral equations, we prove that their solutions depend holomorphically upon perturbations of the arcs’ parametrizations. These results are key to prove the shape (domain) holomorphy of domain-to-solution maps associated to boundary integral equations appearing in uncertainty quantification, inverse problems and deep learning, to name a few applications.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs\",\"authors\":\"José Pinto, Fernando Henríquez, Carlos Jerez-Hanckes\",\"doi\":\"10.1007/s00041-024-10071-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting the corresponding boundary value problems as boundary integral equations, we prove that their solutions depend holomorphically upon perturbations of the arcs’ parametrizations. These results are key to prove the shape (domain) holomorphy of domain-to-solution maps associated to boundary integral equations appearing in uncertainty quantification, inverse problems and deep learning, to name a few applications.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-02-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00041-024-10071-5\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00041-024-10071-5","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

我们为无界二维域中具有多个有限长开弧的二阶偏微分方程所产生的一般弱矢量和超矢量边界积分算子建立了形状全态结果。将相应的边界值问题重铸成边界积分方程后，我们证明了它们的解全态地依赖于弧参数的扰动。这些结果是证明与不确定性量化、逆问题和深度学习等应用中出现的边界积分方程相关的域到解映射的形状（域）全态性的关键。

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

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting the corresponding boundary value problems as boundary integral equations, we prove that their solutions depend holomorphically upon perturbations of the arcs’ parametrizations. These results are key to prove the shape (domain) holomorphy of domain-to-solution maps associated to boundary integral equations appearing in uncertainty quantification, inverse problems and deep learning, to name a few applications.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.