Diff. Geom, Math. Phys., PDE Seminar: Aaron Zeff Palmer

This talk addresses how the calculus-of-variations is applied to non-linear elasticity. In physically realistic classical models, energy-minimizing deformations may not be smooth enough to satisfy the variational Euler-Lagrange equations. However, with a second-gradient model we guarantee sufficient regularity to rigorously prove energy-minimizers satisfy such an equation and maintain incompressibility and/or global injectivity.

The constraints of incompressibility and self-contact introduce subtle challenges of infinite-dimensional non-linear analysis. I will discuss the techniques and assumptions that we use to prove the existence of a distributional pressure for the incompressibility constraint and a measure-valued surface traction for the self-contact constraint. This work was part of my dissertation research done under the supervision of Professor Timothy J. Healey at Cornell University.