报告题目：Nonlinear Korn inequalities on a surface and shell theory

时间与地点：11月16日周四上午10:00 － 12:00；理科楼112

报告人：Maria MALIN, University of Craiova

摘要: A linear Korn inequality on a surface is an estimate of the distance between two surfaces in terms of the corresponding linearized change of metric and change of curvature tensors. We establish several estimates of the distance between two surfaces immersed in the three-dimensional Euclidean space in terms of the distance between their three fundamental forms, measured in various Sobolev norms (see [2]). By imposing appropriate additional geometrical assumptions, we show that the dependence of the third fundamental form can be avoided. These estimates, which can be seen as nonlinear versions of linear Korn inequalities on a surface appearing in the theory of linearly elastic shells, generalize in particular the nonlinear Korn inequality established by P.G. Ciarlet, L. Gratie, and C. Mardare [1]. We also show how these nonlinear Korn inequalities can be applied to the non-linear Koiter shell model and how they can be reduced upon a formal linearization to linear Korn inequalities on a surface, which play a fundamental role in the mathematical analysis of the linear Koiter shell model.

References:

[1] P.G. Ciarlet, L. Gratie, C. Mardare, A nonlinear Korn inequality on a surface,J. Math. Pures Appl. 85 (2006), 2-16.

[2] P.G. Ciarlet, M. Malin, C. Mardare, New nonlinear estimates for surfaces in

terms of their fundamental forms, C. R. Acad. Sci. Paris, Ser. I, 355 (2017), pp.226-231.