Calderón's problem for plaplace type equations
We investigate a generalization of Calderón’s problem of recovering the conductivity coeﬃcient in a conductivity equation from boundary measurements. As a model
equation we consider the pconductivity equation
div σ ∇up−2 ∇u = 0
with 1 < p < ∞, which reduces to the standard conductivity equation when p = 2.
The thesis consists of results on the direct problem, boundary determination and
detecting inclusions. We formulate the equation as a variational problem also when
the conductivity σ may be zero or inﬁnity in large sets. As a boundary determination
result we recover the ﬁrst order derivative of a smooth conductivity on the boundary.
We use the enclosure method of Ikehata to recover the convex hull of an inclusion of
ﬁnite conductivity and ﬁnd an upper bound for the convex hull if the conductivity
within an inclusion is zero or inﬁnite.
Publisher
University of JyväskyläISBN
9789513965761ISSN Search the Publication Forum
14578905Contains publications
 Article I: Brander, T., Kar, M., & Salo, M. (2015). Enclosure method for the pLaplace equation. Inverse Problems, 31(4), 045001. DOI: 10.1088/02665611/31/4/045001
 Article II: Brander, T. (2016). Calderón problem for the 𝑝Laplacian: First order derivative of conductivity on the boundary. Proceedings of the American Mathematical Society, 144(1), 177189. DOI: 10.1090/proc/12681
 Article III: Brander, T., Ilmavirta, J., & Kar, M. Superconductive and insulating inclusions for nonlinear conductivity equations. Preprint.
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