# CONFLUENTES MATHEMATICI

The role of the Hilbert metric in a class of singular elliptic boundary value problems in convex domains
Confluentes Mathematici, Volume 9 (2017) no. 1, pp. 105-117.

In a recent paper [7], we were led to consider a distance over a bounded open convex domain. It turns out to be the so-called Thompson metric, which is equivalent to the Hilbert metric. It plays a key role in the analysis of existence and uniqueness of solutions to a class of elliptic boundary-value problems that are singular at the boundary.

Revised:
Accepted:
Published online:
DOI: 10.5802/cml.38
Classification: 35J75,  52A99
Keywords: Elliptic PDEs, convex domain, Hilbert metric, singular BVP
Denis Serre 1

1 UMPA, UMR 5669, École Normale Supérieure de Lyon, 46 allée d’Italie, 69364 Lyon Cedex 07, France
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Denis Serre. The role of the Hilbert metric in a class of  singular elliptic boundary value problems in convex domains. Confluentes Mathematici, Volume 9 (2017) no. 1, pp. 105-117. doi : 10.5802/cml.38. https://cml.centre-mersenne.org/articles/10.5802/cml.38/

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[7] D. Serre. Gradient estimate in terms of a Hilbert-like distance, for minimal surfaces and Chaplygin gas. Comm. Partial Diff. Equ., 41:774–784, 2016.

[8] C. Walsh. Gauge-reversing maps on cones, and Hilbert and Thompson isometries. Preprint arXiv:1312.7871 [math.MG] (December 2013).

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