Some properties of the torsion function with Robin boundary conditions

Rossano Sannipoli

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arXiv · 2010.07807

Some properties of the torsion function with Robin boundary conditions

Rossano Sannipoli

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Abstract

In this paper we study some properties of the torsion function with Robin boundary conditions. Here we write the shape derivative of the $L^{\infty}$ and $L^p$ norms, for $p\ge 1$, of the torsion function, seen as a functional on a bounded simply connected open set $\Omega \subset \mathbb{R}^n$, and prove that the balls are critical shapes for these functionals, when the volume of $\Omega$ is preserved.

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Rossano Sannipoli. 2020-10-15. Some properties of the torsion function with Robin boundary conditions. https://arxiv.org/abs/2010.07807

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