A weak-strong convergence property and symmetry of minimizers of constrained variational problems in RN

We prove a weak-strong convergence result for functionals of the form ∫RNj(x,u,Du)dx on W1,p, along equiintegrable sequences. We will then use it to study cases of equality in the extended Polya-Szegö inequality and discuss applications of such a result to prove the symmetry of minimizers of a class of variational problems including nonlocal terms under multiple constraints.