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Seminar information archive ～04/03｜Next seminar｜Future seminars 04/04～

Date, time & place	Thursday 16:00 - 17:30 002Room #002 (Graduate School of Math. Sci. Bldg.)

2006/11/21

16:30-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Henrik SHAHGHOLIAN (王立工科大学、ストックホルム)
Composite membrane and the structure of the singular set

[ Abstract ]
In this talk we present our study of the behavior of the singular set

$\\{u=|\\nabla u| =0\\}$ for solutions

$u$ to the free boundary problem

$\\Delta u = f\\chi_{\\{u\\geq 0\\} } -g\\chi_{\\{u<0\\}},$
where

$f$ and

$g$ are H\\"older continuous functions,

$f$ is positive and

$f+g$ is negative. Such problems arise in an eigenvalue optimization for composite membranes.
We show that if for a singular point

$z$ there are

$r_0>0$ , and

$c_0>0$ such that the density assumption

$|\\{u< 0\\}\\cap B_r(z)|\\geq c_0 r2 \\forall r< r_0$
holds, then

$z$ is isolated.

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