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

Denis Serre (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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.

Mots clés: Chaplygin gas; Riemann problem; Keldysh-type degeneracy; Hilbert distance

Domaines: Equations aux dérivées partielles [math.AP]; Mathématiques générales [math.GM]; Mécanique des fluides [physics.class-ph]

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⟩