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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.
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 (267 Kb, last modified 17.5.2013)
References (61 Kb, last modified 17.5.2013)
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