Best constant in weighted sobolev inequality with weights being powers of distance from the origin. Issue 3 (1997) - Horiuchi, Toshio
Abstract : We study the best constant in Sobolev inequality with weights being powers of distance from the origin inℝ n . In this variational problem, the invariance ofℝ n 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.