Date/Time
Date(s) - 25/03/2024
11:30 am - 12:30 pm

Location: HH 207

Speaker: Dominik Stantejsky (McMaster)

Title: A Priori Bounds for Minimizers of Ginzburg-Landau Energy with Divergence Penalization and Tangential Anchoring

Abstract: In this talk, I will present a method to obtain a priori bounds in $L^\infty$ for minimizers of the Ginzburg-Landau energy with an additional quadratic divergence penalization on simply connected domains, subject to tangential boundary conditions. Contrary to the classical Ginzburg-Landau energy, deriving such a bound on a minimizer $u_\epsilon$ is not easily obtained and requires careful estimates close to the boundary due to the lack of a Dirichlet condition. Moreover, as I will show using an example, the typical bound $|u_\epsilon|\leq 1$ cannot hold and needs to be replaced by $|u_\epsilon|\leq C$ for a constant $C>1$. I will then present how such a uniform bound can be obtained, combining reflection techniques, energy estimates and a rescaling argument. Our result also provides regularity for our elliptic system with mixed Dirichlet-Neumann boundary condition.