Ivan G. Avramidi (Department of Mathematics, New Mexico Tech)

ABSTRACT:

The boundary-value problem for Laplace-type operators acting on smooth sections of a vector bundle over a compact Riemannian manifold with nonstandard singular boundary conditions, which include Dirichlet conditions on one part of the boundary and Neumann ones on another part of the boundary, is studied. The condition of strong ellipticity of this boundary-value problem is formulated. The resolvent kernel and the heat kernel in the leading approximation are explicitly constructed. The leading heat kernel asymptotics are computed. It is found that the heat kernel coefficients have additional invariants coming from codimension one submanifolds as well as from the codimension two submanifold as opposed to conventional smooth boundary value problem.
 

Slides of the lecture: PostScript

Preprint: math-ph/0110020