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arXiv · 2509.14648

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

Qinfeng Li·Juncheng Wei·Ruofei Yao
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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., $\beta \geq -\kappa$ on $\partial\Omega$). We also show that this condition is, in a certain sense, sharp by constructing a counterexample.

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Qinfeng Li, Juncheng Wei, Ruofei Yao. 2025-09-18. Monotonicity properties of the Robin torsion function in a class of symmetric planar domains. https://arxiv.org/abs/2509.14648

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