Gradient estimate on convex domains and applications
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- by Feng-Yu Wang and Lixin Yan PDF
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Abstract:
By solving the Skorokhod equation for reflecting diffusion processes on a convex domain, gradient estimates for the associated Neumann semigroup are derived. As applications, functional/Harnack inequalities are established for the Neumann semigroup. When the domain is bounded, the gradient estimates are applied to the study of Riesz transforms and regularity of the inhomogeneous Neumann problems on convex domains.References
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Additional Information
- Feng-Yu Wang
- Affiliation: School of Mathematical Sciences and Laboratory for Mathematical Complex System, Beijing Normal University, Beijing 100875, People’s Republic of China – and – Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, United Kingdom
- Email: wangfy@bnu.edu.cn, F.Y.Wang@swansea.ac.uk
- Lixin Yan
- Affiliation: Department of Mathematics, Sun Yat-sen (Zhongshan) University, Guangzhou, 510275, People’s Republic of China
- MR Author ID: 618148
- Email: mcsylx@mail.sysu.edu.cn
- Received by editor(s): January 23, 2011
- Received by editor(s) in revised form: July 16, 2011
- Published electronically: July 12, 2012
- Additional Notes: The first author is supported by SRFDP, the Fundamental Research Funds for the Central Universities and NNSF of China (Grant No. 11131003).
The second author is supported by NNSF of China (Grant No. 10925106), Guangdong Province Key Laboratory of Computational Science and the Fundamental Research Funds for the Central Universities (Grant No. 09lgzs610). - Communicated by: Marius Junge
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1067-1081
- MSC (2010): Primary 60J75, 60J45; Secondary 42B35, 42B20, 35J25
- DOI: https://doi.org/10.1090/S0002-9939-2012-11480-7
- MathSciNet review: 3003697