5, the constant term of course would result in no vector since there is no directional derivative from au.

alpha] and [beta] are constants and [partial derivative]u/[partial derivative]n represents the directional derivative in the direction normal n to the boundary [partial derivative][OMEGA] which by convention points outwards.

0](x,y) denotes the clark generalized

directional derivative and [partial derivative]f (x,y) denotes the Clarke subdifferential of f at (x,y).

If F is a locally Lipschitzian and nonsmooth function and for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] exists, is said that F'(x,h) is the directional derivative of F.

The one fundamental distinction between the smooth (F-differentiable) and nonsmooth (B-differentiable) functions is the absence of linearity in the directional derivative for nonsmooth functions.

The linear operation G is the

directional derivative of J in the direction [phi].

The difference between the smooth (F-differentiable) and non-smooth (Bdifferentiable) functions is the absence of linearity in the directional derivative for non-smooth functions.

exists, is said that F'(x,h) is the directional derivative of F.

F](t) is a conventional forward difference formula for the directional derivative [T.

B](t) is a standard backward difference approximation of the directional derivative.

for the

directional derivative of [phi] in the direction u.

0](x; v) the Clarke

directional derivative of a vector function F [member of] L([R.