1.

Time: 10th June (Thursday) 11:00 – 12:00

Speaker: Dr. Seongmin Jeon (KTH Royal Institute of Technology)

Place: #746, Natural Science Building, Hanyang University

Title : Almost minimizers for the thin obstacle problem

Abstract:

We consider Anzellotti-type almost minimizers for the thin obstacle (or Signorini) problem with zero thin obstacle. We discuss the regularity of the almost minimizers, as well as the regularity and structure of their free boundaries. The analysis of the free boundary is based on a successful adaptation of energy methods such as a one-parameter family of Weiss-type monotonicity formulas, Almgren-type frequency formula, and the epiperimetric and logarithmic epiperimetric inequalities for the solutions of the thin obstacle problem. This is joint work with Arshak Petrosyan.

2.

Time: 24th June (Thursday) 15:00 – 16:00

Speaker: Prof. Hyungjin Huh (Chung-Ang University)

Place: #746, Natural Science Building, Hanyang University

Title : Gradient flows related with $\alpha$-energy problem

Abstract:

We address a system of ODEs which is related with a particle system whose dynamics is governed by a gradient flow on the unit sphere associated with the $\alpha$ energy interaction potential between positions of all particles measured by a weighted distance $ |x_i -x_k |^{2\alpha + 2}$ for any $\alpha \neq -1$ and $\log |x_i -x_k |^2$ for $\alpha = -1$. Here we are interested in the repulsive coupling to study the equilibrium states and their stability. We mainly consider several case studies to obtain the qualitative insight.