Sharp Trace Inequality for the Fractional Laplacian.

Series: 
Research Horizons Seminar
Wednesday, September 21, 2011 - 12:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Georgia Tech
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.