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| HAL: hal-00176512, version 1 |
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| Journal of Nonlinear and Convex Analysis 2, 3 (2001) 333-343 |
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| Convex Analysis techniques for Hopf-Lax formulae in Hamilton-Jacobi equations |
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| Cyril Imbert 1 |
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| (2001) |
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| The purpose of the present paper is to prove, solely using Convex (and Nonsmooth) analysis techniques, that Hopf-Lax formulae provide explicit solutions for Hamilton-Jacobi equations with merely lower semicontinuous initial data. The substance of these results appears in a paper by Alvarez, Barron and Ishii (1999) but the proofs are fundamentally different (we do not use the comparison principle) and a distinct notion of discontinuous solutions is used. Moreover we give a maximum principle for the Lax function. This approach permits us to fully understand the role of the convexity of the data. |
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| 1: | Mathématiques pour l'Industrie et la Physique (MIP) |
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CNRS : UMR5640 – Université des Sciences Sociales - Toulouse I – Université Paul Sabatier - Toulouse III – Institut National des Sciences Appliquées de Toulouse |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Hopf-Lax functions – Convex analysis – lsc solutions – lsc initial data – epi-sum – Legendre-Fenchel conjugate – Clarke-Ledyaev mean value inequality |
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| hal-00176512, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00176512 | |
| oai:hal.archives-ouvertes.fr:hal-00176512 | |
| From: Cyril Imbert | |
| Submitted on: Wednesday, 3 October 2007 16:45:30 | |
| Updated on: Wednesday, 3 October 2007 17:24:30 | |
