On Optimal Hardy Inequalities in Cones

Abstract

For a given subcritical Schrödinger operator in a cone in ℝn with a given Hardy potential corresponding to the distance to the boundary of the cone, we present an explicit optimal Hardy-type improvement. In particular, we present an explicit expression for the associate best Hardy constant, and for the corresponding ground state.

Keywords

• Ground state
• Hardy inequality
• minimal growth
• positive solutions