|Publication ahead of print|
|Published online||28 September 2017|
Ground states for fractional magnetic operators
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.
Received: 23 June 2016
Revised: 9 November 2016
Accepted: 9 November 2016
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.
Mathematics Subject Classification: 49A50 / 26A33 / 74G65 / 82D99
Key words: Fractional magnetic operators / minimization problems / concentration compactness
© EDP Sciences, SMAI 2017
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