Abstract

We present two new classes of integrands on a ball, with non-linear dependence on the state function for which we have existence of radial minima in Wo 2,p or W2,p ?Wo 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.