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We give a simple proof of the fact that for a large class of quasilinear elliptic equations and systems the solutions that minimize the corresponding energy in the set of all solutions are radially symmetric. We require just continuous nonlinearities and no cooperative conditions for systems. Thus, in particular, our results cannot be obtained by using the moving planes method. In the case of scalar equations, we also prove that any least energy solution has a constant sign and is monotone with respect to the radial variable., Comment: 12 pages

For a large class of variational problems we prove that minimizers are symmetric whenever they are $C^1$., Comment: 17 pages, to appear in Arch. Rational Mech. Anal.; added Example 7 and some references