Uniqueness and radial symmetry of minimizers for a nonlocal variational problem

Abstract

For −n < p < 0, 0 0; 0 ≤ u(x) ≤ M, with given m and M, is proved in [3]. Moreover, except for translation, uniqueness and radial symmetry of the minimizer is proved for −n < p < 0 and q = 2. Here in the present paper, we show that, except for translation, uniqueness and radial symmetry of the minimizer hold for −n < p < 0 and 2 ≤ q ≤ 4. Applications are given.