Steiner symmetrization: a weighted version of Polya - Szego principle

Let us consider a Dirichlet integral of the type F(u) = Z ­ f(Du) dx where u is a nonnegative Sobolev function with compact support in ­. The well known P¶olya-SzegÄo principle states that if us denotes the Steiner symmetrand of u, then: F(us) · F(u): We study the case when the integrand f depends also on x and u