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arXiv · 2105.12979

A Poincar\'e type inequality with three constraints

Gisella Croce·Antoine Henrot
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Abstract

In this paper, we consider a problem in calculus of variations motivated by a quantitative isoperimetric inequality in the plane. More precisely, the aim of this article is the computation of the minimum of the variational problem $$\inf_{u\in\mathcal{W}}\frac{\displaystyle\int_{-\pi}^{\pi}[(u')^2-u^2]d\theta}{\displaystyle\left[\int_{-\pi}^{\pi}|u| d\theta\right]^2}$$where $u\in \mathcal{W}$ is a $H^1(-\pi,\pi)$ periodic function, with zero average on $(-\pi,\pi)$ and orthogonal to sine and cosine.

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Gisella Croce, Antoine Henrot. 2021-05-27. A Poincar\'e type inequality with three constraints. https://arxiv.org/abs/2105.12979

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