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arXiv · 1008.1939

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

Hichem Hajaiej·Stefan Krömer
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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-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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Hichem Hajaiej, Stefan Krömer. 2010-08-11. A weak-strong convergence property and symmetry of minimizers of constrained variational problems in $\mathbb{R}^N$. https://arxiv.org/abs/1008.1939

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