Harnack Inequality for Hypoelliptic Second Order Partial Differential Operators

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• 作者：Alessia E. Kogoj ; Sergio Polidoro
• 关键词：Harnack inequality ; Hypoelliptic operators ; Potential theory
• 刊名：Potential Analysis
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：45
• 期：3
• 页码：545-555
• 全文大小：278 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Potential Theory
  Probability Theory and Stochastic Processes
  Geometry
  Functional Analysis
  
• 出版者：Springer Netherlands
• ISSN：1572-929X
• 卷排序：45

文摘

We consider non-negative solutions \(u:{\Omega }\longrightarrow \mathbb {R}\) of second order hypoelliptic equations$$ \mathcal {L} u(x) =\sum \limits _{i,j=1}^{n} \partial _{x_{i}} \left (a_{ij}(x)\partial _{x_{j}} u(x) \right ) + \sum \limits _{i=1}^{n} b_{i}(x) \partial _{x_{i}} u(x) =0 $$ where Ω is a bounded open subset of \(\mathbb {R}^{n}\) and x denotes the point of Ω. For any fixed x₀ ∈ Ω, we prove a Harnack inequality of this type$$ \sup _{K} u \le C_{K} u(x_{0})\qquad \forall \ u \ \text { s.t. } \ \mathcal {L} u=0, u\geq 0, $$ where K is any compact subset of the interior of the \(\mathcal {L}\)-propagation set ofx₀ and the constant C_K does not depend on u.KeywordsHarnack inequalityHypoelliptic operatorsPotential theoryMathematics Subject Classification (2010)35H1035K1031D05References1.Agrachev, A.A., Sachkov, Y.L.: Control theory from the geometric viewpoint, Encyclopaedia of Mathematical Sciences, vol. 87. Springer-Verlag, Berlin (2004). 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McGraw-Hill Book Co., New York (1987)Copyright information© Springer Science+Business Media Dordrecht 2016Authors and AffiliationsAlessia E. Kogoj1Email authorSergio Polidoro21.Dipartimento di Ingegneria dell’Informazione, Ingegneria Elettrica e Matematica ApplicataUniversità degli Studi di SalernoFisciano (SA)Italy2.Dipartimento di Scienze Fisiche, Informatiche e MatematicheUniversità di Modena e Reggio EmiliaModenaItaly About this article CrossMark Print ISSN 0926-2601 Online ISSN 1572-929X Publisher Name Springer Netherlands 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/s11118-016-9557-y_Harnack Inequality for Hypoellipti", 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/s11118-016-9557-y_Harnack Inequality for Hypoellipti", 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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