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IMA Journal of Applied Mathematics Advance Access originally published online on September 25, 2007
IMA Journal of Applied Mathematics 2007 72(5):563-569; doi:10.1093/imamat/hxm028
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A bound for the optimal constant in an inequality of Ladyzhenskaya and Solonnikov

L. E. Payne{dagger}

Department of Mathematics, Cornell University, Ithaca, NY 14853, USA

{dagger} Email: lep8{at}cornell.edu

Received on July 5, 2006; Accepted on January 22, 2007

Ladyzhenskaya & Solonnikov (1976) introduced a representation theorem in R3, which contained an integral inequality involving a multiplicative dimensionless constant. The existence of the constant was established but not its magnitude which depends only on the shape of the domain. In this paper, we derive an upper bound for the optimal constant when the underlying domain is star shaped.

Keywords: norm inequalities; Velte constant.


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