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Abstract
We study the resolvent for nontrapping obstacles on manifolds with Euclidean ends. It is well known that for such manifolds, the outgoing resolvent satisfies $\\chi R(k) \chi\_{L^2\to L^2}\leq C{k}^{1}$ for ${k}>1$, but the constant $C$ has been little studied. We show that, for high frequencies, the constant is bounded above by $2/\pi$ times the length of the longest generalized bicharacteristic of $\xi_g^21$ remaining in the support of $\chi.$ We show that this estimate is optimal in the case of manifolds without boundary. We then explore the implications of this result for the numerical analysis of the Helmholtz equation.
Original language  English 

Pages (fromto)  157202 
Journal  Pure and Applied Analysis 
Volume  2 
Issue number  1 
Early online date  11 Dec 2019 
DOIs  
Publication status  Published  2020 
Bibliographical note
40 pagesKeywords
 math.AP
 math.NA
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Dive into the research topics of 'Optimal constants in nontrapping resolvent estimates and applications in numerical analysis'. Together they form a unique fingerprint.Projects
 1 Finished

At the interface between semiclassical analysis and numerical analysis of Wave propogation problems
Spence, E. (PI)
Engineering and Physical Sciences Research Council
1/10/17 → 30/09/23
Project: Research council