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Optimal regularity for the Poisson equation
Author(s):
Lihe
Wang;
Fengping
Yao;
Shulin
Zhou;
Huilian
Jia
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2037-2047.
MSC (2000):
Primary 35J05;
Secondary 35J15
Posted:
January 16, 2009
MathSciNet review:
2480285
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Abstract:
In this paper we study the regularity theory for the Poisson equation in  under proper conditions. Furthermore, it will be verified that these conditions are optimal.
References:
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Additional Information:
Lihe
Wang
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Address at time of publication:
Department of Mathematics, Xian Jiaotong University, Xian 710049, People's Republic of China
Email:
lwang@math.uiowa.edu
Fengping
Yao
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China
Email:
yfp@shu.edu.cn
Shulin
Zhou
Affiliation:
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China
Email:
szhou@math.pku.edu.cn
Huilian
Jia
Affiliation:
Department of Mathematics, Xian Jiaotong University, Xian 710049, People's Republic of China
Email:
jiahl@mail.xjtu.edu.cn
DOI:
10.1090/S0002-9939-09-09805-0
PII:
S 0002-9939(09)09805-0
Keywords:
Orlicz space,
Poisson equation,
regularity.
Received by editor(s):
April 23, 2008,
Received by editor(s) in revised form:
July 21, 2008
Posted:
January 16, 2009
Additional Notes:
The first and fourth authors were supported in part by NSF \#0701392 and NSFC 10771166.
The second and third authors were supported in part by the NBRPC under Grant 2006CB705700, the NSFC under Grant 60532080, and the KPCME under Grant 306017.
Communicated by:
Matthew J. Gursky
Copyright of article:
Copyright
2009,
American Mathematical Society
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