Decay estimates for the wave and Dirac equations with a magnetic potential
D'Ancona, Piero ; Fanelli, Luca
arXiv, 0504370 / Harvested from arXiv
Text on arXiv
We study the dispersive properties of the wave equation and the massless Dirac equation in three space dimensions, perturbed with electromagnetic potentials. The potentials are assumed to be small but may be rough. For both equations, we prove a dispersive estimate of the form |u(t,x)|< C/t. The constant C can be estimated in terms of a weighted H^s norm of the data, for suitable values of s. As a consequence of our method of proof, we establish the limiting absorption principle for the massless Dirac operator perturbed with a small, rough matrix potential.
Publié le : 2005-04-18
Classification:  Mathematics - Analysis of PDEs,  Mathematical Physics,  Mathematics - Spectral Theory,  35L05,  58J45 
@article{0504370,
     author = {D'Ancona, Piero and Fanelli, Luca},
     title = {Decay estimates for the wave and Dirac equations with a magnetic
  potential},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504370}
}

D'Ancona, Piero; Fanelli, Luca. Decay estimates for the wave and Dirac equations with a magnetic
  potential. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504370/