4 citations · 5 across the 7 of their papers we have counts for
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Weighted sparsity regularization for source identification for elliptic PDEs
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
This investigation is motivated by PDE-constrained optimization problems arising in connection with electrocardiograms (ECGs) and electroencephalography (EEG). Standard sparsity re…
Modified Tikhonov regularization for identifying several sources
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We study whether a modified version of Tikhonov regularization can be used to identify several local sources from Dirichlet boundary data for a prototypical elliptic PDE. This pape…
A regularization operator for source identification for elliptic PDEs
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We study a source identification problem for a prototypical elliptic PDE from Dirichlet boundary data. This problem is ill-posed, and the involved forward operator has a significan…
Generalized spectrum of second order differential operators
Tomáš Gergelits, Bjørn Fredrik Nielsen, Zdeněk Strakoš
We analyze the spectrum of the operator , where denotes the Laplacian and is a symmetric tensor. Our main result shows that this s…