Ground states for fractional magnetic operators
ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 1, pp. 1-24.

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.

Received:
Accepted:
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, Volume 24 (2018) no. 1, pp. 1-24. doi : 10.1051/cocv/2016071. http://archive.numdam.org/articles/10.1051/cocv/2016071/

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