报告题目：Small perturbations of the type of boundary condition of an elliptic PDE and application to shape optimization

报告时间：2025-05-28   16:30-17:30

报  告 人 ：Prof. Eric Bonnetier （Université Grenoble-Alpes）

报告地点：雷军科技楼六楼报告厅（644）

Abstract：Asymptotic expansions of the solution to an elliptic PDE in the presence of inclusions of small size has been a topic of great interest in the past decades. Indeed, such expansions proved interesting for applications in inverse problems, as a means to build efficient and stable algorithms for detecting inhomogeneities from boundary measurements. In this talk, we study the behavior of the solution to an elliptic equation when the boundary condition is perturbed on a small subset ω_ε of the boundary. We characterize the first term in the asymptotic expansion of the solution, in terms of the relevant measure of smallness of ω_ε, and we give explicit examples when ω_ε is a small surfacic ball in R^d,d=2,3.We use our asymptotic expansions to propose an algorithm for shape optimization problems, when the part of the boundary on which a specific boundary condition is prescribed is itself a design variable. This is joint work with Carlos Brito-Pacheco, Charles Dapogny, Rafael Estevez, and Michael Vogelius.