PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Toan Nguyen, Fei Wang, Hope Shaffer, Mark Levi, Victor Nistor, Jinchao Xu, Ludmil Zikatanov.

Title:Polyconvex integrands in the calculus of variations
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Wilfrid Gangbo, Georgia Institute of Technology
Abstract Link:http://people.math.gatech.edu/~gangbo/
Abstract:
In nonlinear elasticity theory, ones deals with functionals of the form u \to I(u) = \int (W(\nabla u) + u . F), where W is a function de ned on the set of dxd matrices, W(\xi) fails to be a convex function of  but is rather a convex function of the minors of \xi. Motivated by the study of Ogden material we consider functions satisfying lim det_{\xi \to 0+} W(\xi) = \infty$. For these functionals, identifying the Euler-Lagrange equations satis ed by the minimizers of I(.) remains an open outstanding problem in the calculus of variations. Furthermore, the current state of the art in the calculus of variations dramatically fails to predict the uniqueness of the minimizers of I(.) in many interesting cases. In this talk, we introduce a series of problems which we hope will contribute to a better understanding the above issues. This talk is based on a joint work with R. Awi.

Room Reservation Information

Room Number:MB106
Date:12 / 02 / 2013
Time:02:30pm - 03:30pm