The seminar takes place on Fridays, at 14:15 in SR 2.040.
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Upcoming
April 24th at 14:15 in SR 2.040 .
Speaker: Sebastián Flores Sepúlveda
Title: On the shape of the positivity region for a free boundary problem describing cell polarization
Given a smooth bounded domain in three dimensional space, we study a mass-constrained obstacle-type problem posed on its boundary. This problem has been proposed as a model for cell polarization by Matthias Röger, Barbara Niethammer and Juan J. L. Velázquez in 2020. We describe in detail the shape of the positivity set in the generic case where the signal is a Morse function on the surface. As a consequence, we derive regularity of the free boundary for small positive mass. We also obtain scaling limits in more general settings, and we illustrate behavior where the signal is non-generic by way of some examples.
This is joint work with Barbara Niethammer and Juan J. L. Velázquez
