The minimizing problem involving p-Laplacian and Hardy-Littlewood-Sobolev upper critical exponent.

In this paper, we study the minimizing problem ... where ... N and ... is the Hardy- Littlewood-Sobolev upper critical exponent. Firstly, by using refinement of the Hardy- Littlewood-Sobolev inequality, we prove that Sp,1,α,μ is achieved in RN by a radially symmetric, nonincreasing and nonnegative function. Secondly, we give a estimation of extremal function. [ABSTRACT FROM AUTHOR]