Recovering the conductances on grids: A theoretical justification
Visualitza/Obre
Cita com:
hdl:2117/87425
Tipus de documentArticle
Data publicació2016
Condicions d'accésAccés obert
Llevat que s'hi indiqui el contrari, els
continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
:
Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
In this work, we present an overview of the work developed by the
authors in the context of inverse problems on nite networks. This study performs
an extension of the pioneer studies by E.B. Curtis and J.A. Morrow, and
sets the theoretical basis for solving inverse problems on networks. We present
just a glance of what we call overdetermined partial boundary value problems,
in which any data are not prescribed on a part of the boundary, whereas in
another part of the boundary both the values of the function and of its normal
derivative are given. The resolvent kernels associated with these problems are
described and they are the fundamental tool to perform an algorithm for the
recovery of the conductance of a 3{dimensional grid. We strongly believe that
the columns of the partial overdetermined Poisson kernel are the discrete counterpart
of the so{called CGO solutions (complex geometrical optic solutions)
that, in their turn, are the key to solve inverse continuous problems on planar
domains. Finally, we display the steps needed to recover the conductances in
a 3{dimensional grid.
CitacióArauz, C., Carmona, A., Encinas, A., Mitjana, M. Recovering the conductances on grids: A theoretical justification. "Contemporary mathematics", 2016, vol. 658, p. 149-167.
ISSN0271-4132
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
ACEM-Inverse3D.pdf | 446,4Kb | Visualitza/Obre |