by Joonas Ilmavirta, Teemu Saksala and Lili Yan
Abstract:
In this short paper, we show that any Lamé system whose Dirichlet-to-Neumann map for the elastic wave equation agrees with the one arising from the homogeneous Lamé system must actually be homogeneous. We do not need to impose any assumptions for the Lamé coefficients that we aim to recover. We use the fact that the homogeneous system gives rise to a geometry that is both simple and admits a strictly convex foliation.
Reference:
Rigidity of homogeneous Lamé systems (Joonas Ilmavirta, Teemu Saksala and Lili Yan), 2026.
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In this short paper, we show that any Lamé system whose Dirichlet-to-Neumann map for the elastic wave equation agrees with the one arising from the homogeneous Lamé system must actually be homogeneous. We do not need to impose any assumptions for the Lamé coefficients that we aim to recover. We use the fact that the homogeneous system gives rise to a geometry that is both simple and admits a strictly convex foliation.
[arXiv]
Bibtex Entry:
@unpublished{homogeneous-lame-rigidity,
author = {Joonas Ilmavirta and Teemu Saksala and Lili Yan},
title = {{Rigidity of homogeneous Lam\'{e} systems}},
month = feb,
year = 2026,
arxiv = {2602.08860},
url = {http://users.jyu.fi/~jojapeil/pub/homogeneous-lame-rigidity.pdf},
abstract = {In this short paper, we show that any Lam\'{e} system whose Dirichlet-to-Neumann map for the elastic wave equation agrees with the one arising from the homogeneous Lam\'{e} system must actually be homogeneous. We do not need to impose any assumptions for the Lam\'{e} coefficients that we aim to recover. We use the fact that the homogeneous system gives rise to a geometry that is both simple and admits a strictly convex foliation.}
}