Microlocal analysis of scattering data for nested conormal potentials

Details Microlocal analysis of scattering data for nested conormal potentials Microlocal analysis of scattering data for nested conormal potentials

2011-03-30

arxiv.org/abs/1103.6015v2

Mathematics

Analysis of PDEs

52 pages, 1 figure; to appear in Journal of Functional Analysis

Scientific paper

Working in the time domain, we show that the location of the singularities and the principal symbol of a potential that is conormal to nested submanifolds $S_2 \subset S_1 \subset \mathbb{R}^n$, for $n \geq 3$, can be recovered from the backscattering as well as from the restriction of the far-field pattern to more general determined sets of scattering data. This extends the work of Greenleaf and Uhlmann where the potentials considered are conormal to a single submanifold $S \subset \mathbb{R}^n$. We utilize the microlocal analysis of the wave operator $\square=\partial_t^2 - \triangle_x$ and multiplication by a nested conormal distribution in order to study their action on spaces of conormal-like distributions.

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