- Series
- Research Horizons Seminar
- Time
- Wednesday, September 21, 2011 - 12:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Amit Einav – Georgia Tech
- Organizer
- Bulent Tosun
Sharp trace inequalities play a major role in the world of
Mathematics. Not only do they give a connection between 'boundary values' of
the trace and 'interior values' of the function, but also the truest form of
it, many times with a complete classification of when equality is attained.
The result presented here, motivated by such inequality proved by Jose'
Escobar, is a new trace inequality, connecting between the fractional
laplacian of a function and its restriction to the intersection of the
hyperplanes x_(n)=0, x_(n-1)=0, ..., x_(n-j+1)=0 where 1<=j<=n. We will show
that the inequality is sharp and discussed the natural space for it, along
with the functions who attain equality in it.
The above result is based on a joint work with Prof. Michael Loss.