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September 3

No Seminar 

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September 10

Howen Chuah, Purdue University

TITLE : The free Boundary in a higher dimensional Long-Range Segregation Model

ABSTRACT:We consider a system of elliptic equations, depending on a small parameter  $\eps$,  that models long-range segregation of populations. The diffusion is governed by the Laplacian. This system was previously investigated by Caffarelli, Patrizi, and Quitalo  as a model in population dynamics, and they established the regularity of the free boundary in two dimensions. We analyze the free boundary in the higher dimensional case. We extend the concept of angles and asymptotic cones to higher dimensions, and give a characterization of regular and singular points in terms of their densities and angles. We obtain a structure result of the free boundary and show that, if the angles at the singular points are away from $\frac{n\omega_n}{2}$, the regular set is open in the free boundary and locally a $C^1$ manifold of dimension $n-1$. We also show that, if the supports of the populations are convex, they are convex polytopes. A weak form of the equality of angles for the convex configuration is also derived.

Torres

September 17

Qirui Peng, UC Santa Barbara 

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Gismondi

September 24

Mark Allen, BYU 

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Petrosyan

October 1

Kuan-Ting Yeh, Purdue University 

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Torres

October 8

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October 15

Claudia Pena Vazquez, BCAM 

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Gismondi

October 22

Anuk Dayaprema, University of Wisconsin

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Wang

October 29

Yannick Sire, Johns Hopkins University 

Wang

November 5

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November 12

Yunhong Deng, UIC 

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Gao

November 19

Mark Ma, Columbia University 

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Torres

November 26

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December 3

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