Singular Adams inequality for biharmonic operator on Heisenberg Group and its applications

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• 作者：G. Dwivedi ; J. Tyagi
• 关键词：Bi ; Laplacian ; Variational methods ; Singular Adams inequality ; Heisenberg group
• 刊名：NoDEA : Nonlinear Differential Equations and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：23
• 期：6
• 全文大小：787 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-9004
• 卷排序：23

文摘

The goal of this paper is to establish singular Adams type inequality for biharmonic operator on Heisenberg group. As an application, we establish the existence of a solution to$$\Delta_{\mathbb{H}^n}^2 u=\frac{f(\xi,u)}{\rho(\xi)^a}\,\,\text{ in}\Omega,\,\, u|_{\partial\Omega}=0=\left.\frac{\partial u}{\partial\nu}\right|_{\partial\Omega},$$where \({0\in \Omega \subseteq \mathbb{H}^4}\) is a bounded domain, \(0 \leq a \leq Q,\,(Q=10).\) The special feature of this problem is that it contains an exponential nonlinearity and singular potential.KeywordsBi-LaplacianVariational methodsSingular Adams inequalityHeisenberg groupMathematics Subject ClassificationPrimary 35J91Secondary 35B3335R03References1.Adams D.R.: A sharp inequality of J Moser for higher order derivatives. Ann. Math. 128(2), 385–398 (1988)MathSciNetMATHCrossRefGoogle Scholar2.Adams, R.A., Fournier, J.J.F.: Sobolev Spaces, vol. 140. 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Univ. 18(1), 45–52 (2003)MathSciNetMATHCrossRefGoogle ScholarCopyright information© Springer International Publishing 2016Authors and AffiliationsG. Dwivedi1Email authorView author's OrcID profileJ. Tyagi11.Indian Institute of Technology GandhinagarPalaj, GandhinagarIndia About this article CrossMark Print ISSN 1021-9722 Online ISSN 1420-9004 Publisher Name Springer International Publishing About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s00030-016-0412-z_Singular Adams inequality for biha", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s00030-016-0412-z_Singular Adams inequality for biha", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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