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Title: A Mean Value Theorem for non Differentiable Mappings in Banach Spaces
Authors: Deville, Robert
Keywords: Mean Value Theorem
Smooth Variational Principle
Non Smooth Analysis
Viscosity Solutions
Issue Date: 1995
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 21, No 1, (1995), 59p-66p
Abstract: We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which satisfy a coercive condition. This last result slightly improves some earlier work by G. Barles and H. Ishii.
ISSN: 1310-6600
Appears in Collections:Volume 21 Number 1

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