Monotonicity properties of the Robin torsion function in a class of symmetric planar domains

Abstract

We prove the monotonicity property of the Robin torsion function in a smooth planar domain $\Omega$ 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 construct a counterexample showing that the curvature condition cannot, in general, be removed.

15 pages, 2 figures