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On a parabolic equation, involving inverse square potential, defined on the whole space

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Abstract

We study a linear parabolic equation, involving inverse square potential, defined on the whole space. It turns out, that the asymptotic behavior of its solution, is not a decay to the trivial function. For this, we prove new results for the Hardy inequality on \({\mathbb {R}}^N\).

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Authors and Affiliations

  1. Faculty of Sciences, Universiti Brunei Darussalam, Gadong, 1410, Brunei

    Nikolaos B. Zographopoulos

  2. Hellenic Army Academy, Department of Mathematics and Engineering Sciences, University of Military Education, 16673, Vari, Athens, Greece

    Nikolaos B. Zographopoulos

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  1. Nikolaos B. Zographopoulos
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Correspondence to Nikolaos B. Zographopoulos.

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Communicated by J. Ball.

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Zographopoulos, N.B. On a parabolic equation, involving inverse square potential, defined on the whole space. Calc. Var. 59, 79 (2020). https://doi.org/10.1007/s00526-020-01746-0

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  • DOI: https://doi.org/10.1007/s00526-020-01746-0

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