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| HAL: hal-00366901, version 3 |
| arXiv: 0903.1699 |
| DOI: 10.1016/j.jde.2010.07.005 |
| Detailed view |  Export this paper |
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| Journal of Differential Equations 250, 3 (2011) 1553--1574 |
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| Available versions: | v1 (2009-03-10) | v2 (2009-05-16) | v3 (2010-07-30) |
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| Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations |
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| Cyril Imbert 1 |
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| (2011) |
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| In this paper, we study fully non-linear elliptic equations in non-divergence form which can be degenerate when ``the gradient is small''. Typical examples are either equations involving the $m$-Laplace operator or Bellman-Isaacs equations from stochastic control problems. We establish an Alexandroff-Bakelman-Pucci estimate and we prove a Harnack inequality for viscosity solutions of such degenerate elliptic equations. |
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| 1: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| CEREMADE |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Degenerate fully non-linear elliptic equation – singular fully non-linear elliptic equation – non-divergence form – Alexandrov-Bakelman-Pucci estimate – weak Harnack inequality – local maximum principle – Harnack inequality – Hölder regularity – viscosity solutions |
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| hal-00366901, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00366901 | |
| oai:hal.archives-ouvertes.fr:hal-00366901 | |
| From: Cyril Imbert | |
| Submitted on: Thursday, 29 July 2010 12:10:55 | |
| Updated on: Monday, 29 November 2010 10:10:29 | |
