Best constant in weighted sobolev inequality with weights being powers of distance from the origin

Abstract

We study the best constant in Sobolev inequality with weights being powers of distance from the origin in . In this variational problem, the invariance of 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.

Keywords

• Weighted Sobolev inequality
• concentration compactness