The Calderón problem for quasilinear elliptic equations
Günther Uhlmann, Claudio Muñoz
Abstract
In this paper we show uniqueness of the conductivity for the quasilinear Calderón's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself and its gradient. Under some structural assumptions on the direct problem, a real-valued conductivity allowing a small analytic continuation to the complex plane induce a unique Dirichlet-to-Neumann (DN) map. The method of proof considers some complex-valued, linear test functions based on a point of the boundary of the domain, and a linearization of the DN map placed at these particular set of solutions.
Topics & Concepts
UniquenessLinearizationMathematicsMathematical analysisNonlinear systemDomain (mathematical analysis)Plane (geometry)Boundary (topology)Dirichlet distributionComplex planeBoundary value problemInverseApplied mathematicsGeometryPhysicsQuantum mechanicsNumerical methods in inverse problemsAdvanced Mathematical Modeling in EngineeringComposite Material Mechanics