JournalsrlmVol. 33, No. 1pp. 23–37

Some properties of the torsion function with Robin boundary conditions

  • Rossano Sannipoli

    Università degli studi di Napoli Federico II, Italy
Some properties of the torsion function with Robin boundary conditions cover
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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 LL^{\infty} and LpL^p norms, for p1p\ge 1, of the torsion function, seen as a functional on a bounded simply connected open set ΩRn\Omega\subset\mathbb{R}^n, and prove that the balls are critical shapes for these functionals, when the volume of Ω\Omega is preserved.

Cite this article

Rossano Sannipoli, Some properties of the torsion function with Robin boundary conditions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 1, pp. 23–37

DOI 10.4171/RLM/962