Preprint

Inserted: 13 dec 2025
Last Updated: 13 dec 2025

Year: 2025

Abstract:

We prove the monotonicity property of the Robin torsion function in a smooth planar domain with a line of symmetry, provided that the Robin coefficient $\beta$ is greater than or equal to the negative of the boundary curvature $\kappa$ (i.e., $\beta\ge -\kappa$ on $\partial \Omega$ ). We also show that this condition is, in a certain sense, sharp by constructing a counterexample.