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Recent progress in the geometric rigidity of thin domains

Presented by: 
Davit Harutyunyan University of California, Santa Barbara
Date: 
Wednesday 8th May 2019 - 16:20 to 17:00
Venue: 
INI Seminar Room 2
Abstract: 
We will discuss the celebrated geometric rigidity estimate of Friesecke,
James and Mueller. While It is known to be asymptotically sharp for plates in
the thickness vanishing limit, the question for general thin domains is still open.
We will discuss the analogous Korn inequality (the linear version of the rigidity
estimate) and the resolution of it for vector fields under Dirichlet boundary
condition on the domain thin face. We will also present the so called novel Korn
and Geometric Rigidity interpolation inequalities, which solve the question of
best constant in Korn’s second inequality in thin domains; the last had been
unknown since 1908. This is partially joint work with Yury Grabovsky.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons