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arXiv · 1903.04922

Some weighted isoperimetric problems on $\mathbb{R}^N _+ $ with stable half balls have no solutions

Friedemann Brock·Francesco Chiacchio
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Abstract

We show the counter-intuitive fact that some weighted isoperimetric problems on the half-space $ \mathbb{R}^N _+ $, for which half-balls centered at the origin are stable, have no solutions. A particular case is the measure $d\mu = x_N ^{\alpha } \, dx$, with $\alpha \in (-1,0)$. Some results on stability and nonexistence for weighted isoperimetric problems on $\mathbb{R}^N $ are also obtained.

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Friedemann Brock, Francesco Chiacchio. 2019-03-12. Some weighted isoperimetric problems on $\mathbb{R}^N _+ $ with stable half balls have no solutions. https://arxiv.org/abs/1903.04922

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