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• W3153514035 abstract "Abstract We treat an inverse electrical conductivity problem which deals with the reconstruction of nonlinear electrical conductivity starting from boundary measurements in steady currents operations. In this framework, a key role is played by the Monotonicity Principle, which establishes a monotonic relation connecting the unknown material property to the (measured) Dirichlet-to-Neumann operator (DtN). Monotonicity Principles are the foundation for a class of non-iterative and real-time imaging methods and algorithms. In this article, we prove that the monotonicity principle for the Dirichlet Energy in nonlinear problems holds under mild assumptions. Then, we show that apart from linear and p -Laplacian cases, it is impossible to transfer this monotonicity result from the Dirichlet Energy to the DtN operator. To overcome this issue, we introduce a new boundary operator, identified as an average DtN operator." @default.
• W3153514035 created "2021-04-26" @default.
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• W3153514035 date "2021-04-01" @default.
• W3153514035 modified "2023-10-09" @default.
• W3153514035 title "Monotonicity Principle in tomography of nonlinear conducting materials ^*" @default.
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• W3153514035 doi "https://doi.org/10.1088/1361-6420/abd29a" @default.
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