Critical heat kernel estimates via Hardy-Sobolev inequalities

Details Critical heat kernel estimates via Hardy-Sobolev inequalities Critical heat kernel estimates via Hardy-Sobolev inequalities

2003-02-26

arxiv.org/abs/math/0302331v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

We obtain Sobolev inequalities for the Schrodinger operator -\Delta-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.

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