Logarithmic up bounds for solutions of elliptic partial differential equations
Author:
Xiangsheng Xu
Journal:
Proc. Amer. Math. Soc. 139 (2011), 3485-3490
MSC (2010):
Primary 35B50, 35D30; Secondary 35J67, 35J15
DOI:
https://doi.org/10.1090/S0002-9939-2011-10973-0
Published electronically:
June 6, 2011
MathSciNet review:
2813380
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we obtain a logarithmic up bound for the solution to an elliptic mixed boundary value problem. This is an improvement over the corresponding classical result in this area.
- 1. Haïm Brézis and Stephen Wainger, A note on limiting cases of Sobolev embeddings and convolution inequalities, Comm. Partial Differential Equations 5 (1980), no. 7, 773–789. MR 579997, https://doi.org/10.1080/03605308008820154
- 2. Hideo Kozono and Yasushi Taniuchi, Limiting case of the Sobolev inequality in BMO, with application to the Euler equations, Comm. Math. Phys. 214 (2000), no. 1, 191–200. MR 1794270, https://doi.org/10.1007/s002200000267
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Additional Information
Xiangsheng Xu
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
DOI:
https://doi.org/10.1090/S0002-9939-2011-10973-0
Keywords:
Logarithmic up bound,
mixed boundary value problem.
Received by editor(s):
July 7, 2010
Received by editor(s) in revised form:
July 13, 2010
Published electronically:
June 6, 2011
Communicated by:
Walter Craig
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
