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The subdifferential of the sum of two functions in Banach spaces II. Second order case

Published online by Cambridge University Press:  17 April 2009

Robert Deville  and
El Mahjoub El Haddad
Robert Deville
Affiliation:
Université BordeauxlLaboratoire de Mathématiques351, cours del la Libération33400 TalenceFrance
El Mahjoub El Haddad
Affiliation:
Université de Franche-ComtéLaboratoire de Mathématique16, route de Gray25000 BesançonFrance
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Abstract

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We prove a formula for the second order subdifferential of the sum of two lower semi continuous functions in finite dimensions. This formula yields an Alexandrov type theorem for continuous functions. We derive from this uniqueness results of viscosity solutions of second order Hamilton-Jacobi equations and singlevaluedness of the associated Hamilton-Jacobi operators. We also provide conterexamples in infinite dimensional Hilbert spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 2 , April 1995 , pp. 235 - 248
Copyright
Copyright © Australian Mathematical Society 1995

References

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