A weak-strong convergence property and symmetry of minimizers of constrained variational problems in ${\mathbb{R}}^N$

Abstract

We prove a weak-strong convergence result for functionals of the form ${\int }_{{\mathbb{R}}^N}j(x,u,Du)dx$ 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.

25 pages

References in corpus (3)

• Generalized Polya-szego Inequality
• On Symmetry of Minimizers in Constrained Quasi-Linear Problems, 1
• On the necessity of the assumptions used to prove Hardy-Littlewood and Riesz Rearrangement Inequalities 1

Cited by in corpus (1)

• Sufficient and Necessary Conditions for the fractional Gagliardo-Nirenberg Inequalities and applications to Navier-Stokes and generalized boson equations