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

Jacopo Bellazzini, Tohru Ozawa, Nicola Visciglia

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    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
    Volume60
    Issue number3
    DOIs
    Publication statusPublished - 2017 Jan 1

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    Ground State
    Siméon Denis Poisson
    Energy
    Kinetic energy
    Minimization Problem
    Compactness
    Lower bound
    Norm

    Keywords

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

    ASJC Scopus subject areas

    • Analysis
    • Algebra and Number Theory
    • Geometry and Topology

    Cite this

    Ground states for semi-relativistic Schrödinger-Poisson-Slater energy. / Bellazzini, Jacopo; Ozawa, Tohru; Visciglia, Nicola.

    In: Funkcialaj Ekvacioj, Vol. 60, No. 3, 01.01.2017, p. 353-369.

    Research output: Contribution to journalArticle

    Bellazzini, Jacopo ; Ozawa, Tohru ; Visciglia, Nicola. / Ground states for semi-relativistic Schrödinger-Poisson-Slater energy. In: Funkcialaj Ekvacioj. 2017 ; Vol. 60, No. 3. pp. 353-369.
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