Geodesic
Ground states for fractional magnetic operators
d’Avenia, Pietro1  ; Squassina, Marco2
1 Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy.
2 Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via dei Musei 41, 25121 Brescia, Italy.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 1, pp. 1-24

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We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent with the case of absence of magnetic fields. Existence of solutions is obtained via concentration compactness.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016071
Classification : 49A50, 26A33, 74G65, 82D99
Keywords: Fractional magnetic operators, minimization problems, concentration compactness

d’Avenia, Pietro 1 ; Squassina, Marco 2

1 Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy.
2 Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via dei Musei 41, 25121 Brescia, Italy. 
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d’Avenia, Pietro; Squassina, Marco. Ground states for fractional magnetic operators. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 1, pp. 1-24. doi: 10.1051/cocv/2016071

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