For a fractional Hardy-Sobolev minimization problem on a bounded domain with an interior singularity, the optimal constant is attained for parameter values below a threshold and not attained above it.
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A minimization problem involving a fractional Hardy-Sobolev type inequality
For a fractional Hardy-Sobolev minimization problem on a bounded domain with an interior singularity, the optimal constant is attained for parameter values below a threshold and not attained above it.