Chaudhuri, Nirmalendu ; Sandeep, Kunnath
(2004)
*On a heat problem involving the perturbed Hardy–Sobolev operator*
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 134
(4).
pp. 683-693.
ISSN 0308-2105

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Official URL: http://doi.org/10.1017/S0308210500003425

Related URL: http://dx.doi.org/10.1017/S0308210500003425

## Abstract

Let Ω be a bounded domain in Rn, n ≥ 3 and 0 ∈ Ω. It is known that the heat problem ∂u/∂t + Lλ*u = 0 in Ω × (0, ∞), u(x, 0) = u0 ≥ 0, u0 ≢ 0, where Lλ* := −Δ − λ*/|x|2, λ* := ¼(n − 2)2, does not admit any solutions for any t > 0. In this paper we consider the perturbation operator Lλ*q := −Δ − λ*q(x)/|x|2 for some suitable bounded positive weight function q and determine the border line between the existence and non-existence of positive solutions for the above heat problem with the operator Lλ*q. In dimension n = 2, we have similar phenomena for the critical Hardy–Sobolev operator L* := −Δ − (1/4|x|2)(log R/|x|)−2 for sufficiently large R.

Item Type: | Article |
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Source: | Copyright of this article belongs to Cambridge University Press. |

ID Code: | 121272 |

Deposited On: | 13 Jul 2021 09:16 |

Last Modified: | 13 Jul 2021 09:16 |

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