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Title Iterative solutions to the p-Laplace equation arising in hybrid conductivity imaging

Name Alex Timonov
Country USA
Email atimonov@uscupstate.edu
Co-Author(s) none
Submit Time 2014-02-12 08:18:39
Special Session 45: Hybrid imaging methods
The p-Laplace equation (usually for p=0 or p=1) with prescribed boundary conditions is considered as a mathematical model of hybrid conductivity imaging. Due to the absence of convexity (for p < 1) or strict convexity (for p=1) in a variational formulation of the p=Laplace equation, as well as to the singularity at the critical points for p < 2, constructing the stable and computationally efficient algorithms is a challenging problem. In this talk I will present some results of the numerical study of an alternating split Bregman algorithm, as well as the regularised "simple" iterations, with the emphasis on the case p=1 in two and, possibly, three dimensions. This research is a part of the collaborative project with Nachman, Tamasan and Moradifam.