Partial Differential Equations Seminar

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
29 October 2018
16:00
Abstract

We consider vector-valued maps which minimize an energy with two terms: an elastic term penalizing high gradients, and a potential term penalizing values far away from a fixed submanifold N. In the scaling limit where the second term is dominant, minimizers converge to maps with values into the manifold N. If the elastic term is the classical Dirichlet energy (i.e. the squared L^2-norm of the gradient), classical tools show that this convergence is uniform away from a singular set where the energy concentrates. Some physical models (as e.g. liquid crystal models) include however more general elastic energies (still coercive and quadratic in the gradient, but less symmetric), for which these classical tools do not apply. We will present a new strategy to obtain nevertheless this uniform convergence. This is a joint work with Andres Contreras.

  • Partial Differential Equations Seminar
5 November 2018
16:00
Marta Lewicka
Abstract
In this talk, we will present results regarding the regularity and rigidity of solutions to the Monge-Ampere equation, inspired by the role played by this equation in the context of prestrained elasticity. We will show how the Nash-Kuiper convex integration can be applied here to achieve flexibility of Holder solutions, and how other techniques from fluid dynamics (the commutator estimate, yielding the degree formula in the present context) find their parallels in proving the rigidity. We will indicate possible avenues for the future related research.
  • Partial Differential Equations Seminar
Add to My Calendar