Regge-Wheeler Type Equations
Regge-Wheeler Type Equations
This chapter explores estimates for Regge-Wheeler type wave equations used in Theorem M1. It first proves basic Morawetz estimates for ψ. The chapter then proves rp-weighted estimates in the spirit of Dafermos and Rodnianski for ψ. In particular, it obtains as an immediate corollary the proof of Theorem 5.17 in the case s = 0 (i.e., without commutating the equation of ψ with derivatives). It also uses a variation of the method of [5] to derive slightly stronger weighted estimates and prove Theorem 5.18 in the case s = 0. Finally, commuting the equation of ψ with derivatives, the chapter completes the proof of Theorem 5.17 by controlling higher order derivatives of ψ.
Keywords: Regge-Wheeler type equations, wave equations, Morawetz estimates, derivatives, weighted estimates, Theorem M1
Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.
