Pointwise Constraints in Vector-Valued Sobolev Spaces.

We consider a set C<inline-graphic></inline-graphic> with pointwise constraints in a vector-valued Sobolev space. We characterize its tangent and normal cone. Under the additional assumption that the pointwise constraints are affine and satisfy the linear independence constraint qualification, we show that the set C<inline-graphic></inline-graphic> is polyhedric. The results are applied to the optimal control of a string in a polyhedral tube. [ABSTRACT FROM AUTHOR]