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arXiv · 1202.5167

Geometry and Topology of some overdetermined elliptic problems

Antonio Ros·Pieralberto Sicbaldi
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Abstract

We study necessary conditions on the geometry and the topology of domains in $\mathbb{R}^2$ that support a positive solution to a classical overdetermined elliptic problem. The ideas and tools we use come from constant mean curvature surface theory. In particular, we obtain a partial answer to a question posed by H. Berestycki, L. Caffarelli and L. Nirenberg in 1997. We investigate also some boundedness properties of the solution $u$. Some of our results generalize to higher dimensions.

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Antonio Ros, Pieralberto Sicbaldi. 2012-02-23. Geometry and Topology of some overdetermined elliptic problems. https://arxiv.org/abs/1202.5167

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