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arXiv · 2107.05889

Quantitative stability estimates for a two-phase Serrin-type overdetermined problem

Lorenzo Cavallina·Giorgio Poggesi·Toshiaki Yachimura
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Abstract

In this paper, we deal with an overdetermined problem of Serrin-type with respect to a two-phase elliptic operator in divergence form with piecewise constant coefficients. In particular, we consider the case where the two-phase overdetermined problem is close to the one-phase setting. First, we show quantitative stability estimates for the two-phase problem via a one-phase stability result. Furthermore, we prove non-existence for the corresponding inner problem by the aforementioned two-phase stability result.

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Lorenzo Cavallina, Giorgio Poggesi, Toshiaki Yachimura. 2021-07-13. Quantitative stability estimates for a two-phase Serrin-type overdetermined problem. https://arxiv.org/abs/2107.05889

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