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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Gradient estimate on convex domains and applications


Authors: Feng-Yu Wang and Lixin Yan
Journal: Proc. Amer. Math. Soc. 141 (2013), 1067-1081
MSC (2010): Primary 60J75, 60J45; Secondary 42B35, 42B20, 35J25
Published electronically: July 12, 2012
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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.


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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
Email: mcsylx@mail.sysu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11480-7
PII: S 0002-9939(2012)11480-7
Keywords: Gradient estimates for Neumann semigroup, reflecting diffusion process, Neumann problem, Hardy space, Green operator
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.