关于涉及零质量和特鲁丁格-莫泽非线性的 (2,q)- 拉普拉斯平面方程

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-25 DOI:10.1016/j.nonrwa.2024.104227

J.A. Cardoso , J.C. de Albuquerque , J. Carvalho , G.M. Figueiredo

{"title":"关于涉及零质量和特鲁丁格-莫泽非线性的 (2,q)- 拉普拉斯平面方程","authors":"J.A. Cardoso , J.C. de Albuquerque , J. Carvalho , G.M. Figueiredo","doi":"10.1016/j.nonrwa.2024.104227","DOIUrl":null,"url":null,"abstract":"<div><div>In this work, we study existence of positive solutions to a class of <span><math><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-equations in the zero mass case in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. We establish a weighted Sobolev embedding and we introduce a new Trudinger–Moser type inequality. Moreover, since we work on a suitable radial Sobolev space, we prove an appropriate version of the well-known Symmetric Criticality Principle by Palais. Finally, we study regularity of solutions applying Moser iteration scheme.</div></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a planar equation involving (2,q)-Laplacian with zero mass and Trudinger–Moser nonlinearity\",\"authors\":\"J.A. Cardoso , J.C. de Albuquerque , J. Carvalho , G.M. Figueiredo\",\"doi\":\"10.1016/j.nonrwa.2024.104227\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this work, we study existence of positive solutions to a class of <span><math><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-equations in the zero mass case in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. We establish a weighted Sobolev embedding and we introduce a new Trudinger–Moser type inequality. Moreover, since we work on a suitable radial Sobolev space, we prove an appropriate version of the well-known Symmetric Criticality Principle by Palais. Finally, we study regularity of solutions applying Moser iteration scheme.</div></div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-09-25\",\"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://www.sciencedirect.com/science/article/pii/S1468121824001664\",\"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://www.sciencedirect.com/science/article/pii/S1468121824001664","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

在这项工作中，我们研究了 R2 中零质量情况下一类 (2,q) -方程正解的存在性。我们建立了一个加权索波列夫嵌入，并引入了一个新的特鲁丁格-莫泽式不等式。此外，由于我们在合适的径向索波列夫空间上工作，我们证明了帕莱斯著名的对称临界原理的适当版本。最后，我们研究了应用 Moser 迭代方案求解的正则性。

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

On a planar equation involving (2,q)-Laplacian with zero mass and Trudinger–Moser nonlinearity

In this work, we study existence of positive solutions to a class of

(2, q)

-equations in the zero mass case in

R^{2}

. We establish a weighted Sobolev embedding and we introduce a new Trudinger–Moser type inequality. Moreover, since we work on a suitable radial Sobolev space, we prove an appropriate version of the well-known Symmetric Criticality Principle by Palais. Finally, we study regularity of solutions applying Moser iteration scheme.

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.