The Ellipticity of the Elliptic Membrane
Peng‐Fei Yao · Acta Analysis Functionalis Applicata · 2001
We consider the ellipticity of the elliptic membrane. We here show that being clamped on the whole boundary is not necessary for the ellipticity to be true. In particular, we provides two kinds of boundary conditions, called partially free and conjugal. respectively, which make the ellipticity hold for an elliptic membrane without being clamped on the entire boundary. Especially, those results rectify a mistake. made by Slicaru. On the ellipticity of the middle surface of a shell, C. R. Acad. Sci. Paris, t. 322. Serie, p. 97-100. 1996. Finally, we give an example of an elliptic membrane to show that the space of the displacement vectors of the elliptic membrane with the strain energy finite can be very large if we do not place any restriction on it's boundary.