Dispersive estimates for massive Dirac operators in dimension two

M. Burak Erdoğan, William R. Green, Ebru Toprak

Research output: Contribution to journalArticlepeer-review

Abstract

We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the t−1 decay rate holds in the L1→L setting if the threshold energies are regular. We also show these bounds hold in the presence of s-wave resonances at the threshold. We further show that, if the threshold energies are regular then a faster decay rate of t−1(log⁡t)−2 is attained for large t, at the cost of logarithmic spatial weights. The free Dirac equation does not satisfy this bound due to the s-wave resonances at the threshold energies.

Original languageEnglish (US)
Pages (from-to)5802-5837
Number of pages36
JournalJournal of Differential Equations
Volume264
Issue number9
DOIs
StatePublished - May 5 2018

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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