For an improved Hardy-Sobolev inequality on a ball, minimizers exist and are non-radial when the boundary-singular weight parameter a is close to 1, while for small a the infimum equals the classical constant and is not attained.
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Minimization problem associated with an improved Hardy-Sobolev type inequality
For an improved Hardy-Sobolev inequality on a ball, minimizers exist and are non-radial when the boundary-singular weight parameter a is close to 1, while for small a the infimum equals the classical constant and is not attained.