Journal of Inequalities and Applications
Volume 1 (1997), Issue 3, Pages 275-292
doi:10.1155/S1025583497000180
Best constant in weighted sobolev inequality with weights being powers of distance from the origin
Department of Mathematical Science, Ibaraki University, Mito, Ibaraki 310, Japan
Received 16 June 1996
Copyright © 1997 Toshio Horiuchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the best constant in Sobolev inequality with weights being powers of distance from the origin in ℝn. In this variational problem, the invariance of ℝn
by the group of dilatations
creates some possible loss of compactness. As a result we will see that the existence of extremals
and the value of best constant essentially depends upon the relation among parameters in the
inequality.