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The multidirectional mean value inequalities with second order information

Part of: Existence theories Calculus on manifolds; nonlinear operators Measures, integration, derivative, holomorphy

Published online by Cambridge University Press:  09 April 2009

Mohammed Bachir
Mohammed Bachir
Affiliation:
Laboratoire de Mathématiques, Université Bordeaux I, 351, cours de la Libération, 33405 Talence Cedex, France, e-mail: [email protected]
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Abstract

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We give a multidirectional mean value inequality with second order information. This result extends the classical Clarke-Ledyaev's inequality to the second order. As application, we give the uniqueness of viscosity solution of second order Hamilton-Jacobi equations in finite dimensions.

Keywords

mean value inequalityviscosity subdifferentialbump functionHamilton-Jacobi equation.

MSC classification

Secondary: 49J52: Nonsmooth analysis 46G05: Derivatives 49J50: Fréchet and Gateaux differentiability 58C20: Differentiation theory (Gateaux, Fréchet, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 2 , April 2006 , pp. 159 - 172
Copyright
Copyright © Australian Mathematical Society 2006

References

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