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Applied Analysis

Seminar information archive ~04/03Next seminarFuture 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=|nablau|=0 for solutions u to the free boundary problem
Deltau=fchiugeq0gchiu<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 r0>0, and c0>0 such that the density assumption
|u<0capBr(z)|geqc0r2forallr<r0
holds, then z is isolated.