Abstract
Motivated by the Hardy-Sobolev inequality with multiple Hardy potentials, we consider the following minimization problem :
where
, Ω is a smooth domain,
,
,
and
. Concerning the coefficients of Hardy potentials, we derive a sharp threshold for the existence and non-existence of a minimizer. In addition, we study the existence and non-existence of a positive solution to the Euler-Lagrangian equations corresponding to the minimization problems.
Disclosure statement
No potential conflict of interest was reported by the author(s).