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

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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Contributor : Denis Serre <>
Submitted on : Thursday, November 24, 2016 - 4:01:46 PM
Last modification on : Thursday, January 11, 2018 - 6:12:31 AM
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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, Taylor & Francis, 2016, 41, pp.774 - 784. ⟨10.1080/03605302.2015.1127969⟩. ⟨ensl-01402393⟩

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