Journal of Inequalities and Applications
Volume 1 (1997), Issue 3, Pages 275-292
doi:10.1155/S1025583497000180
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.