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

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

2010-08-11

arxiv.org/abs/1008.1939v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

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-Szeg\"o 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.

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