| Abstract: |
| We discuss a framework for treating the inverse obstacle problem for nonlinear elliptic equations with nonlinear materials. The framework is based on two recent theoretical results for nonlinear partial elliptic PDEs: the p-Laplace Signature (p-LS) and the Monotonicity Principle (MP).
The first result (p-LS) allows to model the solution of an elliptic PDE with nonlinear materials in terms of a proper p-Laplace equation, which captures the essence of the problem. The Monotonicity Principle (MP), recently extended to nonlinear materials, provides a monotonic relationship between the material property and the measured quantity (the average Dirichlet-to-Neumann map) that can be `inverted` to find the shape of anomalies.
Numerical examples are provided to show and confirm the effectiveness of the strategy. |
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