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On the ellipticity of linear membrane shell equations. (English) Zbl 0870.73037

Existence and uniqueness of the solution for the membrane shell equations are shown in the case of uniformly elliptic middle surface with smooth boundary. Uniform ellipticity means that the second fundamental tensor is uniformly positive definite. The main part of the paper is devoted to a new proof of a “rigid displacement lemma” which says that a uniformly elliptic membrane allows no bending if the boundary is clamped.
Reviewer: A.Pomp (Stuttgart)

MSC:

74K15 Membranes
35Q72 Other PDE from mechanics (MSC2000)
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