Some properties of the torsion function with Robin boundary conditions

2020/10/15 by Rossano Sannipoli, Sannipoli, Rossano
Mathematics · #35J05 #35J15 #35J20 #35J25 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2010.07807

openalex publication_date 2020/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^∞ and L^p norms, for p≥ 1, of the torsion function, seen as a functional on a bounded simply connected open set Ω⊂ ℝⁿ, and prove that the balls are critical shapes for these functionals, when the volume of Ω is preserved.

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