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The Sobolev norm of characteristic functions with applications to the Calderón inverse problem

AuthorsFaraco, Daniel; Rogers, Keith M.
KeywordsProblemas inversos
Espacios de Sobolev
Issue Date31-Jan-2012
PublisherOxford University Press
CitationQuarterly Journal of Mathematics 64(1) : 133-147(2008)
AbstractWe consider Calderón's inverse problem on planar domains Ω with conductivities in fractional Sobolev spaces. When Ω is Lipschitz, the problem was shown to be stable in the L2-sense in Clop et al. [Stability of calderón's inverse conductivity problem in the plane for discontinuous conductivities, Inverse Probl. Imaging 4 (2010), 49–91]. We remove the Lipschitz condition on the boundary. To this end, we analyse the Sobolev regularity of the characteristic function of Ω. For Ω a quasiball, we compute ||χΩ||Ws,p(ℝd) in terms of the δ-neighbourhoods of the boundary.
Publisher version (URL)http://dx.doi.org/10.1093/qmath/har039
Appears in Collections:(ICMAT) Artículos
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