Sergio Conti, Wednesdays 12-14, Mathematikzentrum, Room 1.008, Thursdays 12-14, Mathematikzentrum, Room 1.007.
First examination: Oral, 19-22 July 2013.
Second examination: Oral, 9-13 September 2013. Precise times will be fixed in the second half of August.
Announcement (889 Kb, last modified 4.3.2013)
The first part of the class is devoted to variational models for the elastic properties of thin sheets. After a brief introduction on continuum mechanics, we shall discuss membrane and plate theories, and their derivations from three-dimensional nonlinear elasticity in the appropriate scaling regimes. The key mathematical tools will be Gamma convergence theory and rigidity estimates.
In the second part of the class we shall address isoperimetric and, more in general, partition problems. The key mathematical toolswe shall develop is the theory functions of bounded variations and sets of finite perimeter.
Required background includes basic measure theory, elementary PDE theory and functional analysis (modules V2B1, V2B2 and V3B1). Some knowledge of the content of the classes PDE and Modeling (V3B2) and Advanced Topics in Analysis and Calculus of Variations - Multiscale Methods in the Calculus of Variations (V5B5, WS 2012-13) is helpful but not a prerequisite, as the necessary notions will be briefly summarized in the class.
The course is coordinated with the lecture course "Numerical Methods for thin elastic sheets, shapes and isoperimetric problems" by M. Rumpf (V5E3, Wednesday 10-12, Thursday 10-12) intending to show the strong interplay between the analytical and computational approaches. Each of these courses will be self contained and can be followed independently. We believe, however, that there will be a substantial gain following both courses in parallel.
Lecture notes (644 Kb, last modified 18.7.2013) References (89 Kb, last modified 18.7.2013)