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On a nonlinear geometrical inverse problem of Signorini type: Identifiability and stability. (English) Zbl 0936.35189
Of concern here are inverse problems, which consist of determining the shape of a part of the unknown boundary given the homogeneous Dirichlet condition on a part of the known boundary and the normal derivative (flux) over the remaining known part of the boundary. On the unknown part of the boundary a further condition of Signorini type is assumed, namely \(u\frac{\partial u}{\partial n} = 0\). The authors prove a uniqueness result i.e. two different admissible boundaries can not produce the same distribution for the field on a set of positive measure contained in the known part of the boundary. They also derive stability theorems using Holmgren’s theorem and Green’s theorem.

35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
74M15 Contact in solid mechanics
31A25 Boundary value and inverse problems for harmonic functions in two dimensions
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