In this paper, we first deduce the following Sobolev inequality with logarithmic term: sup{integral(B) vertical bar u vertical bar(2)*vertical bar ln (tau + vertical bar u vertical bar)vertical bar(vertical bar x vertical bar beta) dx : u is an element of H-0,rad(1)(B), parallel to del u parallel to(L2(B)) = 1} < infinity, (0.1) B (0.1) where beta > 0, tau >= 0 are constants, B is the unit ball in R-N, N >= 3, and 2* = 2N/ (N - 2) is the critical Sobolev exponent. Then we show that the supremum in (0.1) is attained when 0 < beta < min{N/2, N - 2} and 1 0 in B, (0.2) u = 0 on partial derivative...
