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Article Dans Une Revue Journal of Differential Equations Année : 2020

Schrödinger operators with Leray-Hardy potential singular on the boundary

Huyuan Chen
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Résumé

We study the kernel function of the operator u → L µ u = −∆u + µ |x| 2 u in a bounded smooth domain Ω ⊂ R N + such that 0 ∈ ∂Ω, where µ ≥ − N 2 4 is a constant. We show the existence of a Poisson kernel vanishing at 0 and a singular kernel with a singularity at 0. We prove the existence and uniqueness of weak solutions of L µ u = 0 in Ω with boundary data ν + kδ 0 , where ν is a Radon measure on ∂Ω \ {0}, k ∈ R and show that this boundary data corresponds in a unique way to the boundary trace of positive solution of L µ u = 0 in Ω.
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Dates et versions

hal-02157156 , version 1 (15-06-2019)
hal-02157156 , version 2 (19-06-2019)
hal-02157156 , version 3 (25-02-2020)

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Citer

Huyuan Chen, Laurent Veron. Schrödinger operators with Leray-Hardy potential singular on the boundary. Journal of Differential Equations, 2020, 269, pp.2091-2131. ⟨10.1016/j.jde.2020.01.029⟩. ⟨hal-02157156v3⟩
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