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Critical heat kernel estimates via Hardy-Sobolev inequalities

G. Barbatis·S. Filippas·A. Tertikas
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Abstract

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.

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G. Barbatis, S. Filippas, A. Tertikas. 2003-02-26. Critical heat kernel estimates via Hardy-Sobolev inequalities. https://arxiv.org/abs/math/0302331

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