Geodesic
Partial differential equations/Functional analysis
Bourgain–Brézis–Mironescu formula for magnetic operators
[Formule de Brézis–Bourgain–Mironescu pour des opérateurs magnétiques]

Présenté par : Haïm Brézis

Squassina, Marco1 ; Volzone, Bruno2
1 Dipartimento di Informatica, Università degli Studi di Verona, Strada Le Grazie 15, 37134 Verona, Italy
2 Dipartimento di Ingegneria, Università di Napoli Parthenope, Centro Direzionale Isola C/4, 80143 Napoli, Italy
Comptes Rendus. Mathématique, Tome 354 (2016) no. 8, pp. 825-831.

Voir la notice de l'article provenant de la source Numdam

We prove a Bourgain–Brézis–Mironescu-type formula for a class of nonlocal magnetic spaces, which builds a bridge between a fractional magnetic operator recently introduced and the classical theory.

On démontre une formule du type Bourgain–Brézis–Mironescu pour une classe d'espaces magnétiques non locaux, qui jette un pont entre un opérateur magnétique fractionnaire récemment introduit et la théorie classique.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.04.013

Squassina, Marco 1 ; Volzone, Bruno 2

1 Dipartimento di Informatica, Università degli Studi di Verona, Strada Le Grazie 15, 37134 Verona, Italy
2 Dipartimento di Ingegneria, Università di Napoli Parthenope, Centro Direzionale Isola C/4, 80143 Napoli, Italy 
@article{CRMATH_2016__354_8_825_0,
     author = {Squassina, Marco and Volzone, Bruno},
     title = {Bourgain{\textendash}Br\'ezis{\textendash}Mironescu formula for magnetic operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {825--831},
     publisher = {Elsevier},
     volume = {354},
     number = {8},
     year = {2016},
     doi = {10.1016/j.crma.2016.04.013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2016.04.013/}
}
TY  - JOUR
AU  - Squassina, Marco
AU  - Volzone, Bruno
TI  - Bourgain–Brézis–Mironescu formula for magnetic operators
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 825
EP  - 831
VL  - 354
IS  - 8
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2016.04.013/
DO  - 10.1016/j.crma.2016.04.013
LA  - en
ID  - CRMATH_2016__354_8_825_0
ER  - 
%0 Journal Article
%A Squassina, Marco
%A Volzone, Bruno
%T Bourgain–Brézis–Mironescu formula for magnetic operators
%J Comptes Rendus. Mathématique
%D 2016
%P 825-831
%V 354
%N 8
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2016.04.013/
%R 10.1016/j.crma.2016.04.013
%G en
%F CRMATH_2016__354_8_825_0
Squassina, Marco; Volzone, Bruno. Bourgain–Brézis–Mironescu formula for magnetic operators. Comptes Rendus. Mathématique, Tome 354 (2016) no. 8, pp. 825-831. doi : 10.1016/j.crma.2016.04.013. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2016.04.013/

[1] Arioli, G.; Szulkin, A. A semilinear Schrödinger equation in the presence of a magnetic field, Arch. Ration. Mech. Anal., Volume 170 (2003), pp. 277-295

[2] Avron, J.; Herbst, I.; Simon, B. Schrödinger operators with magnetic fields. I. General interactions, Duke Math. J., Volume 45 (1978), pp. 847-883

[3] Bourgain, J.; Brezis, H.; Mironescu, P. Another look at Sobolev spaces (Menaldi, J.L.; Rofman, E.; Sulem, A., eds.), Optimal Control and Partial Differential Equations. A Volume in Honor of Professor Alain Bensoussan's 60th Birthday, IOS Press, Amsterdam, 2001, pp. 439-455

[4] Bourgain, J.; Brezis, H.; Mironescu, P. Limiting embedding theorems for Ws,p when s↑1 and applications, J. Anal. Math., Volume 87 (2002), pp. 77-101

[5] Brasco, L.; Parini, E.; Squassina, M. Stability of variational eigenvalues for the fractional p-Laplacian, Discrete Contin. Dyn. Syst., Ser. A, Volume 36 (2016), pp. 1813-1845

[6] d'Avenia, P.; Squassina, M. Ground states for fractional magnetic operators | arXiv

[7] Evans, L.C. Partial Differential Equations, Graduate Series in Mathematics, American Mathematical Society, 2010

[8] Frank, R.L.; Lieb, E.H.; Seiringer, R. Hardy–Lieb–Thirring inequalities for fractional Schrödinger operators, J. Amer. Math. Soc., Volume 21 (2008), pp. 925-950

[9] Ichinose, T. Magnetic relativistic Schrödinger operators and imaginary-time path integrals, Mathematical Physics, Spectral Theory and Stochastic Analysis, Operator Theory: Advances and Applications, vol. 232, Birkhäuser/Springer, Basel, Switzerland, 2013, pp. 247-297

[10] Maz'ya, V.; Shaposhnikova, T. On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces, J. Funct. Anal., Volume 195 (2002), pp. 230-238

[11] Reed, M.; Simon, B. Methods of Modern Mathematical Physics, I, Functional Analysis, Academic Press, Inc., New York, 1980

Cité par Sources :