We consider a minimizing problem associated with a critical Hardy type inequality involving a mean oscillation. We first introduce a dilation-invariant critical Hardy type inequality which contains a nonlocal term and then analyze the associated Euler–Lagrange equation with the aid of the scaling argument. We prove the nonexistence of minimizers for 1<p<∞ and the existence for p=1.
|Number of pages||18|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 2015 Dec 1|
- Primary 26D10
- Secondary 35J20
ASJC Scopus subject areas
- Applied Mathematics