{"title":"The linear elasticity system under singular forces","authors":"","doi":"10.1016/j.aml.2024.109258","DOIUrl":null,"url":null,"abstract":"<div><p>We study the linear elasticity system under singular forces. We show the existence and uniqueness of solutions in two frameworks: weighted Sobolev spaces <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>ϖ</mi><mo>,</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>, where the weight belongs to the Muckenhoupt class <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and standard Sobolev spaces <span><math><mrow><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span>, where the integrability index <span><math><mi>p</mi></math></span> is less than <span><math><mrow><mi>d</mi><mo>/</mo><mrow><mo>(</mo><mi>d</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. We also propose a standard finite element scheme and provide optimal error estimates in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>–norm.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924002787","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We study the linear elasticity system under singular forces. We show the existence and uniqueness of solutions in two frameworks: weighted Sobolev spaces , where the weight belongs to the Muckenhoupt class , and standard Sobolev spaces , where the integrability index is less than . We also propose a standard finite element scheme and provide optimal error estimates in the –norm.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.