Work

Sharp estimates for the Laplacian torsional rigidity with negative Robin boundary conditions

Year: 2026

Type: article

Abstract: Motivated by pioneering works of Bandle and Wagner, given a bounded Lipschitz domain with , we consider the Robin–Laplacian torsional rigidity with negative boundary parameter and we show that sharp inequalities for hold if is small enough. In particular, we prove that, if is smaller than the first non‐trivial Steklov–Laplacian eigenvalue, then the ball maximises among all convex domains under perimeter or volume constraints. This solves an open problem raised in [5]. We also prove the result in the planar case among simply connected sets and under perimeter constraint.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70407

Authors: Nunzia Gavitone, David Krejčiřík, Gloria Paoli

Institutions: University of Naples Federico II, Czech Technical University in Prague

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni