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
Full-text PDF
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. H. Brezis and S. Wainger, A note on limiting cases of Sobolev embedding and convolution inequalities, Comm. Partial Differential Equations, 5(1980), pp. 773-789. MR 579997 (81k:46028)
- 2. H. Kozono and Y. Taniuchi, Limiting case of the Sobolev inequality in BMO with application to the Euler equations, Commun. Math. Phys., 214(2000), pp. 191-200. MR 1794270 (2002k:46081)
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35B50, 35D30, 35J67, 35J15
Retrieve articles in all journals with MSC (2010): 35B50, 35D30, 35J67, 35J15
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.
