A minimization problem involving a fractional Hardy-Sobolev type inequality
Abstract
In this work, we obtain an existence of nontrivial solutions to a minimization problem involving a fractional Hardy-Sobolev type inequality in the case of inner singularity. Precisely, for λ>0 we analyze the attainability of the optimal constant μα, λ():=∈f\ [u]2s,+λ∫|u|2 \, dx u∈ Hs(), \, ∫ |u(x)|2s,α|x|α \, dx=1 \, where 0<s<1, n>4s, 0<α<2s, 2s,α=2(n-α)n-2s, and ⊂ Rn be a bounded domain such that 0∈ .
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