Comptes Rendus
no. 8
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

Marco Squassina1 ; Bruno Volzone2
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, Volume 354 (2016) no. 8, pp. 825-831.

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.

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.

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

Marco Squassina 1 ; Bruno Volzone 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 
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Marco Squassina; Bruno Volzone. Bourgain–Brézis–Mironescu formula for magnetic operators. Comptes Rendus. Mathématique, Volume 354 (2016) no. 8, pp. 825-831. doi : 10.1016/j.crma.2016.04.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.04.013/

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

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

[3] J. Bourgain; H. Brezis; P. Mironescu Another look at Sobolev spaces (J.L. Menaldi; E. Rofman; A. Sulem, 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] J. Bourgain; H. Brezis; P. Mironescu Limiting embedding theorems for Ws,p when s↑1 and applications, J. Anal. Math., Volume 87 (2002), pp. 77-101

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

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

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

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

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

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

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