Critical heat kernel estimates via Hardy-Sobolev inequalities

Barbatis, G.; Filippas, S.; Tertikas, A.

Critical heat kernel estimates via Hardy-Sobolev inequalities

Authors

Barbatis, G.

Filippas, S.

Tertikas, A.

Description

We obtain Sobolev inequalities for the Schrodinger operator -Δ-V, where V has critical behaviour V(x)=((N-2)/2)^2|x|^{-2} near the origin. We apply these inequalities to obtain pointwise estimates on the associated heat kernel, improving upon earlier results.
23 pages