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Journal Articles Communications in Partial Differential Equations Year : 2016

Gradient estimate in terms of a Hilbert-like distance, for minimal surfaces and Chaplygin gas

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Abstract

We consider a quasilinear elliptic boundary value problem with homogenenous Dirich-let condition. The data is a convex planar domain. The gradient estimate is needed to ensure the uniform ellipticity, before applying regularity theory. We establish this estimate in terms of a distance which is equivalent to the Hilbert metric. This fills the proof of existence and uniqueness of a solution to this BVP, when the domain is only convex but not strictly, for instance if it is a polygon.
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Dates and versions

ensl-01402393 , version 1 (24-11-2016)

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Denis Serre. Gradient estimate in terms of a Hilbert-like distance, for minimal surfaces and Chaplygin gas. Communications in Partial Differential Equations, 2016, 41, pp.774 - 784. ⟨10.1080/03605302.2015.1127969⟩. ⟨ensl-01402393⟩
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