Electron. J. Diff. Eqns., Vol. 2003(2003), No. 43, pp. 1-8.

Hardy inequalities with boundary terms

Zhi-Qiang Wang & Meijun Zhu

Abstract:
In this note, we present some Hardy type inequalities for functions which do not vanish on the boundary of a given domain. We establish these inequalities for both bounded and unbounded domains and also obtain the best embedding constants in these inequalities for special domains. Our results are motivated by and building upon some recent work in [5, 6, 9, 12].

Submitted December 2, 2002. Published April 16, 2003.
Math Subject Classifications: 35J20, 35J25.
Key Words: Hardy inequality with boundary terms, weighted versions of Hardy inequality.

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Zhi-Qiang Wang
Department of Mathematics and Statistics
Utah State University
Logan, Utah 84322-3900, USA
email: wang@math.usu.edu

Meijun Zhu
Department of Mathematics
University of Oklahoma
Norman, Oklahoma 73019, USA
email: mzhu@math.ou.edu

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