We give a complete classification of radially symmetric self-similar solutions of the equation ut = Δlog u, u > 0, in higher dimensions. For any n > 2, η > 0, a, β ∈ R, we prove that there exists a radially symmetric solution for the corresponding elliptic equation Aogv+av+/3x'Vv = 0, v > 0, inKn, v(0) = TJ, if and only if either a > 0 or 0 > 0. For n > 3, we prove that linv-.oo r2v(r) = 2(n - 2)/(a - 2/3) if a > max(2/3,O) and limr-.^ r2v(r)/logr = 2(n-2)//3 if a = 2/3 > 0. For n > 2 and 2/3 > max(a,0), we prove that lim,->oaTa^v(r) = A for some constant A > 0.
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