Minimization problem associated with an improved Hardy-Sobolev type inequality

We consider the existence or non-existence of a minimizer of the following minimization problems associated with an improved Hardy–Sobolev type inequality introduced by Ioku (2019): Ia≔infu∈W01,p(BR)∖{0}∫BR|∇u|pdx∫BR|u|p∗(s)Va(x)dxpp∗(s),whereVa(x)=1|x|s1−a|x|RN−pp−1β≥1|x|s, where 1更多