弹性和可压缩弹性中p$ p$ -生长泛函的(高频)唯一性准则

IF 1.8 3区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Elasticity Pub Date : 2023-02-22 DOI:10.1007/s10659-023-09996-7

Marcel Dengler

{"title":"弹性和可压缩弹性中p$ p$ -生长泛函的(高频)唯一性准则","authors":"Marcel Dengler","doi":"10.1007/s10659-023-09996-7","DOIUrl":null,"url":null,"abstract":"<div>In this work our main objective is to establish various (high frequency-) uniqueness criteria. Initially, we consider \$p\$-Dirichlet type functionals on a suitable class of measure preserving maps \$u: B\\subset \\mathbb{R}^{2} \\to \\mathbb{R}^{2}\$, \$B\$ being the unit disk, and subject to suitable boundary conditions. In the second part we focus on a very similar situations only exchanging the previous functionals by a suitable class of \$p\$-growing polyconvex functionals and allowing the maps to be arbitrary.In both cases a particular emphasis is laid on high pressure situations, where only uniqueness for a subclass, containing solely of variations with high enough Fourier-modes, can be obtained.</div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"(High Frequency-) Uniqueness Criteria for \\\$p\\\$-Growth Functionals in in- and Compressible Elasticity\",\"authors\":\"Marcel Dengler\",\"doi\":\"10.1007/s10659-023-09996-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>In this work our main objective is to establish various (high frequency-) uniqueness criteria. Initially, we consider \\\$p\\\$-Dirichlet type functionals on a suitable class of measure preserving maps \\\$u: B\\\\subset \\\\mathbb{R}^{2} \\\\to \\\\mathbb{R}^{2}\\\$, \\\$B\\\$ being the unit disk, and subject to suitable boundary conditions. In the second part we focus on a very similar situations only exchanging the previous functionals by a suitable class of \\\$p\\\$-growing polyconvex functionals and allowing the maps to be arbitrary.In both cases a particular emphasis is laid on high pressure situations, where only uniqueness for a subclass, containing solely of variations with high enough Fourier-modes, can be obtained.</div>\",\"PeriodicalId\":624,\"journal\":{\"name\":\"Journal of Elasticity\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-02-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Elasticity\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10659-023-09996-7\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Elasticity","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10659-023-09996-7","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

在这项工作中，我们的主要目标是建立各种（高频）唯一性标准。起初，我们考虑的是$p$-Dirichlet 类型的函数，这些函数是在一类合适的度量保全映射 $u: B\subset \mathbb{R}^{2} \to \mathbb{R}^{2}$上，$B$是单位盘，并受制于合适的边界条件。在第二部分中，我们将重点放在非常类似的情况上，只是用一类合适的 $p$-growing polyconvex 函数来交换之前的函数，并允许映射是任意的。在这两种情况下，我们都特别强调高压情况，在高压情况下，只有包含具有足够高傅里叶模的变化的子类才能获得唯一性。

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

(High Frequency-) Uniqueness Criteria for $p$-Growth Functionals in in- and Compressible Elasticity

In this work our main objective is to establish various (high frequency-) uniqueness criteria. Initially, we consider $p$-Dirichlet type functionals on a suitable class of measure preserving maps $u: B\subset \mathbb{R}^{2} \to \mathbb{R}^{2}$, $B$ being the unit disk, and subject to suitable boundary conditions. In the second part we focus on a very similar situations only exchanging the previous functionals by a suitable class of $p$-growing polyconvex functionals and allowing the maps to be arbitrary.

In both cases a particular emphasis is laid on high pressure situations, where only uniqueness for a subclass, containing solely of variations with high enough Fourier-modes, can be obtained.

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

Journal of Elasticity 工程技术-材料科学：综合

CiteScore

3.70

自引率

15.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.