Composite media, almost touching disks and the maximum principle https://arxiv.org/abs/2507.02077 #mathAP
We consider the setting of two disks in a domain in $\mathbb{R}^2$ which are almost touching and have finite and positive conductivities, giving rise to a divergence form elliptic equation with discontinuous coefficients. We use the maximum principle to give a new proof of a gradient bound of Li-Vogelius.
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