Critical heat kernel estimates via Hardy-Sobolev inequalities

A. Tertikas; G. Barbatis; S. Filippas

arxiv: math/0302331 · v1 · submitted 2003-02-26 · 🧮 math.AP · math.SP

Critical heat kernel estimates via Hardy-Sobolev inequalities

G. Barbatis , S. Filippas , A. Tertikas This is my paper

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keywords inequalitiescriticalestimatesheatkernelobtainapplyassociated

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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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Critical heat kernel estimates via Hardy-Sobolev inequalities

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