Critical heat kernel estimates via Hardy-Sobolev inequalities
Analysis of PDEs
2007-05-23 v1 Spectral Theory
Abstract
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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Cite
@article{arxiv.math/0302331,
title = {Critical heat kernel estimates via Hardy-Sobolev inequalities},
author = {G. Barbatis and S. Filippas and A. Tertikas},
journal= {arXiv preprint arXiv:math/0302331},
year = {2007}
}
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23 pages