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.
