Affiliation:
1. Department of Mathematics and Science Education , 7928 University of South-Eastern Norway , Postboks 4, 3199 Borre , Norway
2. Institute for Mathematical Sciences , Norwegian University of Science and Technology , Trondheim , Norway
Abstract
Abstract
We recover the conductivity σ at the boundary of a domain from a combination of Dirichlet and Neumann boundary data and generalized power/current density data at the boundary, from a single quite arbitrary set of data, in AET or CDII.
The argument is elementary, algebraic and local.
More generally, we consider the variable exponent
p
(
⋅
)
{p(\,\cdot\,)}
-Laplacian as a forward model with the interior density data
σ
|
∇
u
|
q
{\sigma|\nabla u|^{q}}
, and find out that single measurement specifies the boundary conductivity when
p
-
q
≥
1
{p-q\geq 1}
, and otherwise the measurement specifies two alternatives.
We present heuristics for selecting between these alternatives.
Both p and q may depend on the spatial variable x, but they are assumed to be a priori known.
We illustrate the practical situations with numerical examples with the code available.
Funder
Danmarks Frie Forskningsfond
Norges Forskningsråd
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