Remarks on bounded solutions of steady Hamilton-Jacobi equations

Gawtum Namah; Mihai Bostan

hal-00476301, version 1

Remarks on bounded solutions of steady Hamilton-Jacobi equations

Gawtum Namah () ¹, Mihai Bostan ^1, 2, 3

Comptes Rendus de l Académie des Sciences - Series I - Mathematics 15-16, 347 (2009) 873-878

Abstract: We study here the equation $H(Du) = H(0), x \in \R ^N$. More precisely we investigate under which hypotheses the constant functions are the only bounded solutions. In arbitrary space dimension we prove that this happens when strict convexity and coercivity occur. In one space dimension we show that the above property holds true for hamiltonians in a larger class. These results apply when studying the long time behaviour of solutions for time-dependent Hamilton-Jacobi equations.

1: Laboratoire de Mathématiques (LM-Besançon)
CNRS : UMR6623 – Université de Franche-Comté
2: CALVI (INRIA Nancy - Grand Est / IECN / LSIIT / IRMA)
CNRS : UMR7005 – INRIA – Université de Strasbourg – Université de Lorraine
3: Institut Elie Cartan Nancy (IECN)
CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)

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http://hal.archives-ouvertes.fr/hal-00476301
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From: Gawtum Namah <>
Submitted on: Thursday, 6 May 2010 16:52:38
Updated on: Monday, 9 May 2011 15:08:21

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