Remarks on Differentiability of Metric Projections onto Cones of Nonnegative Functions

The differentiability properties of the metric projections onto the cones of nonnegative functions in

and in

W^{1,p}(0,1) W 1 , p ( 0 , 1 )

are considered. It is shown that the metric projection mapping is Bouligand differentiable in

L^p(0,1) L p ( 0 , 1 )

, but it is not Bouligand differentiable in

W^{1,p}(0,1) W 1 , p ( 0 , 1 )

.