Dispersive estimates for the Dirac equation in an Aharonov-Bohm field

被引：12
作者：
Cacciafesta, F. [1 ]
Fanelli, L. [2 ]
机构：
[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via R Cozzi,53, I-20125 Milan, Italy
[2] SAPIENZA Univ Roma, Dipartimento Matemat, Ple A Moro 5, I-00185 Rome, Italy
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 07期
关键词：
Dirac equation; Magnetic potentials; Local smoothing; SCHRODINGER-EQUATIONS; GLOBAL EXISTENCE; BESSEL-FUNCTIONS; TIME-DECAY; WAVE; POTENTIALS;
D O I：
10.1016/j.jde.2017.05.018
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove local smoothing and weighted Strichartz estimates for the Dirac equation with a Aharonov-Bohm potential. The proof, inspired by [12], relies on an explicit representation of the solution built in terms of spectral projections. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：4382 / 4399
页数：18
相关论文
共 37 条
  • [1] SIGNIFICANCE OF ELECTROMAGNETIC POTENTIALS IN THE QUANTUM THEORY
    AHARONOV, Y
    BOHM, D
    [J]. PHYSICAL REVIEW, 1959, 115 (03): : 485 - 491
  • [2] [Anonymous], 1992, TEXTS MONOGR PHYS
  • [3] On the lack of dispersion for a class of magnetic Dirac flows
    Arrizabalaga, Naiara
    Fanelli, Luca
    Garcia, Andoni
    [J]. JOURNAL OF EVOLUTION EQUATIONS, 2013, 13 (01) : 89 - 106
  • [4] COUNTEREXAMPLE TO THE PARAMAGNETIC CONJECTURE
    AVRON, J
    SIMON, B
    [J]. PHYSICS LETTERS A, 1979, 75 (1-2) : 41 - 42
  • [5] Virial identity and weak dispersion for the magnetic Dirac equation
    Boussaid, Nabile
    D'Ancona, Piero
    Fanelli, Luca
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2011, 95 (02): : 137 - 150
  • [6] Burq N, 2004, INDIANA U MATH J, V53, P1665
  • [7] Strichartz estimates for the wave and Schrodinger equations with the inverse-square potential
    Burq, N
    Planchon, F
    Stalker, JG
    Tahvildar-Zadeh, AS
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 203 (02) : 519 - 549
  • [8] Cacciafesta F., WEAK DISPERSION WEIG
  • [9] Local smoothing estimates for the massless Dirac-Coulomb equation in 2 and 3 dimensions
    Cacciafesta, Federico
    Sere, Eric
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 271 (08) : 2339 - 2358
  • [10] Endpoint estimates and global existence for the nonlinear Dirac equation with potential
    Cacciafesta, Federico
    D'Ancona, Piero
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (05) : 2233 - 2260
1234