Gradient estimates and applications for Neumann semigroup on narrow strip

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• 作者：Feng-Yu Wang
• 关键词：Neumann semigroup ; Narrow strip ; Gradient estimate ; Log ; Harnack inequality ; Heat kernel ; 60J60 ; 58G32
• 刊名：Mathematische Zeitschrift
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：282
• 期：1-2
• 页码：43-60
• 全文大小：515 KB
• 参考文献：1. Bakry, D.: $\text{ L }^{\prime }$hypercontractivité et son utilisation en théorie des semigroups. Lectures on Probability Theory, Lecture Notes in Math, vol. 1581, pp. 1-114. Springer, Berlin (1994)
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  9. Léandre, R.: Long-time behaviour for the Brownian heat kernel on a compact Riemannian manifold and Bismut’s integration-by-parts formula. Seminar on Stochastic Analysis, Random Fields and Applications V, 197C201, Progr. Probab., 59, Birkhäuser, Basel (2008)
  10. Röckner, M., Wang, F.-Y.: Log-Harnack inequality for Stochastic differential equations in Hilbert spaces and its consequences. Infin. Dimens. Anal. Quant. Probab. Relat. Top. 13, 27-37 (2010)CrossRef
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  13. Wang, F.-Y.: Gradient and Harnack inequalities on noncompact manifolds with boundary. Pac. J. Math. 245, 185-200 (2010)CrossRef
  14. Wang, F.-Y.: Semigroup properties for the second fundamental form. Doc. Math. 15, 543-559 (2010)
  15. Wang, F.-Y.: Analysis for Diffusion Processes on Riemannian Manifolds. World Scientific, Singapore (2013)CrossRef
  16. Wang, F.-Y., Yuan, C.: Harnack inequalities for functional SDEs with multiplicative noise and applications. Stoch. Process. Appl. 121, 2692-2710 (2011)MathSciNet CrossRef
  17. Wang, J.: Global heat kernel estimates. Pac. J. Math. 178, 377-398 (1997)CrossRef
  
• 作者单位：Feng-Yu Wang (1) (2)
  
  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China
  2. Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1823

文摘

By using local and global versions of Bismut type derivative formulas, gradient estimates are derived for the Neumann semigroup on a narrow strip. Applications to functional/cost inequalities and heat kernel estimates are presented. Since the narrow strip we consider is non-convex with zero injectivity radius, and does not satisfy the volume doubling condition, existing results in the literature do not apply. Keywords Neumann semigroup Narrow strip Gradient estimate Log-Harnack inequality Heat kernel