Two-term spectral asymptotics for the Dirichlet Laplacian and its fractional powers

Math Physics Seminar
Wednesday, April 6, 2011 - 4:30pm
1 hour (actually 50 minutes)
Skiles 006
University of Stuttgart
We study the sum of the negative eigenvalues of the Dirichlet Laplace operatoron a bounded domain in the semiclassical limit. We give a new proof thatyields not only the Weyl term but also the second asymptotic term involvingthe surface area of the boundary of the domain.The proof is valid under weak smoothness assumptions on the boundary and theresult can be extended to non-local, non-smooth operators like fractionalpowers of the  Dirichlet Laplacian.(This is joint work with Rupert L. Frank.)