an:01129862
Zbl 0895.73042
Lions, J.-L.; Sanchez-Palencia, E.
On some spaces in the shell theory and on sensitivity
FR
Cioranescu, Doina (ed.) et al., Homogenization and applications to material sciences. Proceedings of the international conference, Nice, France, June 6--10, 1995. Tokyo: Gakkotosho. GAKUTO Int. Ser., Math. Sci. Appl. 9, 271-278 (1995).
1995
a
74K15 35Q72
thin shells; pre-Hilbertian norms; spaces of smooth vector functions; two-dimensional manifolds; completion procedure; dual space; Lax-Milgram problem
Summary: The theory of thin shells leads to the definition of pre-Hilbertian norms (i.e. norms for which the space is not complete) on certain spaces of smooth vector functions defined on two-dimensional manifolds. In certain cases, the completion procedure goes out of the space of distributions. Correspondingly, the dual space does not contain the space of infinitely differentiable functions with compact support, and some kind of instability appears in the Lax-Milgram problem, which is said to be sensitive. A general theorem of sensitivity is proved.
For the entire collection see [Zbl 0873.00028].