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

Jacopo Bellazzini, Tohru Ozawa, Nicola Visciglia

    Research output: Contribution to journalArticle

    3 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)353-369
    Number of pages17
    JournalFunkcialaj Ekvacioj
    Issue number3
    Publication statusPublished - 2017 Jan 1


    • Concentration-compactness
    • Ground states
    • Semi-relativistic Schrödinger equation

    ASJC Scopus subject areas

    • Analysis
    • Algebra and Number Theory
    • Geometry and Topology

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