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.
Accepté le :
DOI : 10.1051/cocv/2016071
Keywords: Fractional magnetic operators, minimization problems, concentration compactness
d’Avenia, Pietro 1 ; Squassina, Marco 2
@article{COCV_2018__24_1_1_0,
author = {d{\textquoteright}Avenia, Pietro and Squassina, Marco},
title = {Ground states for fractional magnetic operators},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1--24},
year = {2018},
publisher = {EDP Sciences},
volume = {24},
number = {1},
doi = {10.1051/cocv/2016071},
mrnumber = {3764131},
zbl = {1400.49059},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2016071/}
}
TY - JOUR AU - d’Avenia, Pietro AU - Squassina, Marco TI - Ground states for fractional magnetic operators JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1 EP - 24 VL - 24 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2016071/ DO - 10.1051/cocv/2016071 LA - en ID - COCV_2018__24_1_1_0 ER -
%0 Journal Article %A d’Avenia, Pietro %A Squassina, Marco %T Ground states for fractional magnetic operators %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1-24 %V 24 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2016071/ %R 10.1051/cocv/2016071 %G en %F COCV_2018__24_1_1_0
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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