TY - JOUR
T1 - The local calderòn problem and the determination at the boundary of the conductivity
AU - Alessandrini, Giovanni
AU - Gaburro, Romina
PY - 2009/8
Y1 - 2009/8
N2 - We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body Ω ⊂ ℝn when the so-called Dirichlet-to-Neumann map is locally given on a non empty portion Γ of the boundary ∂Ω. We extend results of uniqueness and stability at the boundary, obtained by the same authors in SIAM J. Math. Anal. 33:153-171, where the Dirichlet-to-Neumann map was given on all of ∂Ω instead. We also obtain a pointwise stability result at the boundary among the class of conductivities which are continuous at some point y ∈ Γ. Our arguments also apply when the local Neumann-to-Dirichlet map is available.
AB - We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body Ω ⊂ ℝn when the so-called Dirichlet-to-Neumann map is locally given on a non empty portion Γ of the boundary ∂Ω. We extend results of uniqueness and stability at the boundary, obtained by the same authors in SIAM J. Math. Anal. 33:153-171, where the Dirichlet-to-Neumann map was given on all of ∂Ω instead. We also obtain a pointwise stability result at the boundary among the class of conductivities which are continuous at some point y ∈ Γ. Our arguments also apply when the local Neumann-to-Dirichlet map is available.
KW - Anisotropic conductivity
KW - Inverse boundary problems
KW - Local measurements
UR - http://www.scopus.com/inward/record.url?scp=70449480583&partnerID=8YFLogxK
U2 - 10.1080/03605300903017397
DO - 10.1080/03605300903017397
M3 - Article
AN - SCOPUS:70449480583
SN - 0360-5302
VL - 34
SP - 918
EP - 936
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 8
ER -