English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the inverse boundary value problem of determining a coefficientfunction in an elliptic partial differential equation from knowledge of theassociated Neumann-Dirichlet-operator. The unknown coefficient function isassumed to be piecewise constant with respect to a given pixel partition, andupper and lower bounds are assumed to be known a-priori.  We will show that this Calder\'on problem with finitely many unknowns can beequivalently formulated as a minimization problem for a linear cost functionalwith a convex non-linear semidefinite constraint. We also prove error estimatesfor noisy data, and extend the result to the practically relevant case offinitely many measurements, where the coefficient is to be reconstructed from afinite-dimensional Galerkin projection of the Neumann-Dirichlet-operator.  Our result is based on previous works on Loewner monotonicity and convexityof the Neumann-Dirichlet-operator, and the technique of localized potentials.It connects the emerging fields of inverse coefficient problems andsemidefinite optimization.

The Calder\'on problem with finitely many unknowns is equivalent to convex semidefinite optimization