Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - University of Rouen Normandy

Asymptotic expansions of the solution to an elliptic PDE in the presence of inclusions of small size
have found succesfull applications in inverse problems, in particular for the detection of inhomogeneities.
In this talk, we consider situations where the perturbations are not caused by internal inhomogeneities,
but take place on the boundary. Building up on previous work, we assume that a homogeneous Dirichlet or
Neumann boundary condition is replaced by a Robin condition on a small subset $\omega_\varepsilon$ of
the domain boundary.
We characterize the first term in the asymptotic expansion of the solution, in terms of the relevant measure
of smallness of $\omega_\varepsilon$, and study how the convergence of the expansion depends on the
impedance of the Robin boundary condition.
This is joint work with Charles Dapogny (Sorbonne Universit\’e) and Roman Moskalenko (Université
Grenoble-Alpes).