Global Strichartz estimates for nontrapping perturbations of the Laplacian
Hart Smith, Christopher D. Sogge
TL;DR
This work addresses global Strichartz estimates for nontrapping, spatially compact perturbations of the Laplacian in odd dimensions. The authors synthesize exponential energy decay for compact data with local Strichartz estimates and the Minkowski global bound, using a near/far-field decomposition to extend known estimates to exterior-domain perturbations. A key contribution is showing that homogeneous estimates imply inhomogeneous ones via a Christ–Kiselev-type argument, enabling a complete global Strichartz theory for the perturbed wave equation. The results advance the understanding of wave dispersion in nontrapping geometries and provide a robust framework for exterior-domain scattering problems with Dirichlet conditions.
Abstract
The authors prove global Strichartz estimates for compact perturbations of the wave operator in odd dimensions when a non-trapping assumption is satisfied.