# A Mean Value Theorem for non Differentiable Mappings in Banach Spaces

Serdica Mathematical Journal (1995)

- Volume: 21, Issue: 1, page 59-66
- ISSN: 1310-6600

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topDeville, Robert. "A Mean Value Theorem for non Differentiable Mappings in Banach Spaces." Serdica Mathematical Journal 21.1 (1995): 59-66. <http://eudml.org/doc/11657>.

@article{Deville1995,

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.},

author = {Deville, Robert},

journal = {Serdica Mathematical Journal},

keywords = {Mean Value Theorem; Smooth Variational Principle; Non Smooth Analysis; Viscosity Solutions; smooth variational principle; lower semicontinuous function; Banach space; Lipschitz continuous function; subgradients; regularity; viscosity supersolutions; Hamilton-Jacobi equations},

language = {eng},

number = {1},

pages = {59-66},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {A Mean Value Theorem for non Differentiable Mappings in Banach Spaces},

url = {http://eudml.org/doc/11657},

volume = {21},

year = {1995},

}

TY - JOUR

AU - Deville, Robert

TI - A Mean Value Theorem for non Differentiable Mappings in Banach Spaces

JO - Serdica Mathematical Journal

PY - 1995

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 21

IS - 1

SP - 59

EP - 66

AB - 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.

LA - eng

KW - Mean Value Theorem; Smooth Variational Principle; Non Smooth Analysis; Viscosity Solutions; smooth variational principle; lower semicontinuous function; Banach space; Lipschitz continuous function; subgradients; regularity; viscosity supersolutions; Hamilton-Jacobi equations

UR - http://eudml.org/doc/11657

ER -

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