Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A direct linear inversion for discontinuous elastic parameters recovery
  from internal displacement information only   The aim of this paper is to present and analyze a new direct method for
solving the linear elasticity inverse problem. Given measurements of some
displacement fields inside a medium, we show that a stable reconstruction of
elastic parameters is possible, even for discontinuous parameters and without
boundary information. We provide a general approach based on the weak
definition of the stiffness-to-force operator which conduces to see the problem
as a linear system. We prove that in the case of shear modulus reconstruction,
we have an $L^2$-stability with only one measurement under minimal smoothness
assumptions. This stability result is obtained though the proof that the linear
operator to invert has closed range. We then describe a direct discretization
which provides stable reconstructions of both isotropic and anisotropic
stiffness tensors.

13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat