Geometry and Topology of some overdetermined elliptic problems

By A. Ros, P. Sicbaldi. 2012

52 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f18c31907fef78e2f3739c0048e7367c0cc1eec7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. D. Ruiz
2. A. Ros
3. P. Sicbaldi
4. W. H. Meeks
5. Xianhua Tang
6. Sitong Chen
7. Joaquín Pérez
8. Gongbao Li

In Computational Theory and Mathematics

1. D. Ruiz
2. A. Ros
3. P. Sicbaldi
4. Xianhua Tang
5. Sitong Chen
6. Gongbao Li
7. Xiaoyutao Luo
8. Huan-Song Zhou

Citations in the corpus

• Classification of the Solutions to an Overdetermined Elliptic Problem in the Plane (2014, unknown): “Sicbaldi in a very interesting paper [22].”
• A Rigidity Result for Overdetermined Elliptic Problems in the Plane (2015, methodology): “This procedure has also been applied to elliptic problems in half-planes in [11] and to overdetermined problems in [28].”