On a class of elliptic differential operators degenerating at one point
Convergence of special Green integrals for matrix factorization of the Laplace operator in is proved. Explicit formulae for solutions of -equation in strictly pseudo-convex domains in are obtained.
We prove the analog of the Cwikel-Lieb-Rozenblum estimate for a wide class of second-order elliptic operators by two different tools: Lieb-Thirring inequalities for Schrödinger operators with matrix-valued potentials and Sobolev inequalities for warped product spaces.