## Rocky Mountain Journal of Mathematics

### Low regularity ray tracing for wave equations with Gaussian beams

Alden Waters

#### Abstract

We prove observability estimates for oscillatory Cauchy data modulo a small kernel for $n$-dimensional wave equations with space and time dependent $C^2$ and $C^{1,1}$ coefficients using Gaussian beams. We assume the domains and observability regions are in $\mathbb {R}^n$, and the GCC applies. This work generalizes previous observability estimates to higher dimensions and time dependent coefficients. The construction for the Gaussian beamlets solving $C^{1,1}$ wave equations represents an improvement and simplification over Waters (2011).

#### Article information

Source
Rocky Mountain J. Math., Volume 49, Number 3 (2019), 1005-1027.

Dates
First available in Project Euclid: 23 July 2019

https://projecteuclid.org/euclid.rmjm/1563847245

Digital Object Identifier
doi:10.1216/RMJ-2019-49-3-1005

Mathematical Reviews number (MathSciNet)
MR3983312

Zentralblatt MATH identifier
07088348

#### Citation

Waters, Alden. Low regularity ray tracing for wave equations with Gaussian beams. Rocky Mountain J. Math. 49 (2019), no. 3, 1005--1027. doi:10.1216/RMJ-2019-49-3-1005. https://projecteuclid.org/euclid.rmjm/1563847245

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