Patrick Bernard
Place du Marechal de Lattre de Tassigny, 75775 Paris Cedex 16, France
Universite Paris-Dauphine – CEREMADE (UMR 7534)
Publications:
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Bernard P.
The Siegel – Bruno Linearization Theorem
2023, vol. 28, nos. 4-5, pp. 756-762
Abstract
The purpose of this paper is a pedagogical one. We provide a short and selfcontained
account of Siegel’s theorem, as improved by Bruno, which states that a holomorphic
map of the complex plane can be locally linearized near a fixed point under certain conditions
on the multiplier. The main proof is adapted from Bruno’s work.
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Bernard P.
Semi-concave Singularities and the Hamilton–Jacobi Equation
2013, vol. 18, no. 6, pp. 674-685
Abstract
We study the Cauchy problem for the Hamilton–Jacobi equation with a semiconcave initial condition.We prove an inequality between two types of weak solutions emanating from such an initial condition (the variational and the viscosity solution).We also give conditions for an explicit semi-concave function to be a viscosity solution. These conditions generalize the entropy inequality characterizing piecewise smooth solutions of scalar conservation laws in dimension one.
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