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

We prove a weak–strong convergence result for functionals of the form ∫ R N j ( x , u , D u ) d x on W 1 , 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.