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

 

Global estimates in Orlicz spaces for the gradient of solutions to parabolic systems


Authors: Sun-Sig Byun and Seungjin Ryu
Journal: Proc. Amer. Math. Soc. 138 (2010), 641-653
MSC (2000): Primary 35K40, 35R05; Secondary 46E30, 46E35
Published electronically: October 5, 2009
MathSciNet review: 2557181
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Abstract: We find not only an optimal regularity requirement on the coefficients, but also a lowest level of regularity on the boundary for the global estimate of the gradient of a parabolic system in the setting of Orlicz spaces.


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Additional Information

Sun-Sig Byun
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea
Email: byun@snu.ac.kr

Seungjin Ryu
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea
Email: sjryu@math.snu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10094-1
PII: S 0002-9939(09)10094-1
Keywords: Gradient estimate, Orlicz space, parabolic system, maximal function, covering lemma, Reifenberg domain
Received by editor(s): May 8, 2009
Published electronically: October 5, 2009
Additional Notes: This work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-314-C00024).
Communicated by: Tatiana Toro
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.