Critical heat kernel estimates for Schrödinger operators via Hardy-Sobolev inequalities |
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Authors: | G. Barbatis S. Filippas |
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Affiliation: | a Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece b Department of Applied Mathematics, University of Crete, 71409 Heraklion, Greece c Department of Mathematics, University of Crete, 71409 Heraklion, Greece d Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion, Greece |
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Abstract: | We obtain Sobolev inequalities for the Shcrödinger 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 point-wise estimates on the associated heat kernel, improving upon earlier results. |
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Keywords: | 35K65 26D10 (35K20 35B05) |
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