On radial solutions to non-convex variational problems

We present two new classes of integrands on a ball, with nonlinear dependence on the state function for which we have existence of radial minima in W-0(2,p) or W-2,W-p boolean AND W-0(1,p). The integrands studied here define functionals which are lower semicontinuous only along some special minimizing sequences and are non-differentiable. Some qualitative properties of the minima are described and an obstacle problem is treated.