Analysis Seminar

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A nonlocal isoperimetric problem with dipolar repulsion

Speaker: Thilo Simon, NJIT

Location: Warren Weaver Hall 1302

Date: Thursday, April 19, 2018, 11 a.m.

Synopsis:

We study a functional in which perimeter and regularized dipolar repulsion compete under a volume constraint.

In contrast to previously studied similar problems, the nonlocal term contributes to the perimeter term to leading order for small regularization parameters.

Indeed, below a critical value for the dipolar strenght, the limiting functional is a renormalized perimeter and for small, positive regularization parameters the minimizers are balls.
At critical dipolar strength, we identify the next-order Gamma-limit and prove that there exist masses for which minimizers are not balls.

Furthermore, we establish existence of generalized minimizers for all parameters and give conditions for existence of classical minimizers.