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math.AP2018
Optimal constants in nontrapping resolvent estimates and applications in numerical analysis
Jeffrey Galkowski, Euan A. Spence, Jared Wunsch
We study the resolvent for nontrapping obstacles on manifolds with Euclidean ends. It is well known that for such manifolds, the outgoing resolvent satisfies $\|χR(k) χ\|_{L^2\to L…
math.AP2018
Wavenumber-explicit regularity estimates on the acoustic single- and double-layer operators
Jeffrey Galkowski, Euan A. Spence
We prove new, sharp, wavenumber-explicit bounds on the norms of the Helmholtz single- and double-layer boundary-integral operators as mappings from $L^2(\partial Ω)\rightarrow H^1(…
math.AP2018
The Helmholtz equation in random media: well-posedness and a priori bounds
O. R. Pembery, E. A. Spence
We prove well-posedness results and a priori bounds on the solution of the Helmholtz equation , posed either in or in the exte…