Ground states for semi-relativistic Schrödinger-Poisson-Slater energy

Jacopo Bellazzini, Tohru Ozawa, Nicola Visciglia

    研究成果: Article

    3 引用 (Scopus)

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    We prove the existence of ground states for the semi-relativistic Schrödinger- Poisson-Slater energy (Formula presented) α, β > 0 and ρ > 0 is small enough. The minimization problem is L2 critical and in order to characterize the values α, β > 0 such that Iα, β(ρ) > –∞ for every ρ > 0, we prove a new lower bound on the Coulomb energy involving the kinetic energy and the exchange energy. We prove the existence of a constant S > 0 such that (Formula presented) for all φ ∈ C0 (R3). Besides, we show that similar compactness property fails if we replace the inhomogeneous Sobolev norm ║u║2 H1/2(R3) by the homogeneous one ║u║1/2(R3) in the energy above.

    元の言語English
    ページ(範囲)353-369
    ページ数17
    ジャーナルFunkcialaj Ekvacioj
    60
    発行部数3
    DOI
    出版物ステータスPublished - 2017 1 1

    ASJC Scopus subject areas

    • Analysis
    • Algebra and Number Theory
    • Geometry and Topology

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