Applied Analysis
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.) |
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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
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=fchiugeq0−gchiu<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.
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=fchiugeq0−gchiu<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.