“Perturbations near the vertex of a plane sector and a 3D cone”
Thursday May 13, 2021 at 11:30 am - Zoom - Matteo Dalla Riva (University of Tulsa, visiting scientist at our Department)
The Functional Analytic Approach (FAA) is a method to study boundary value problems in singularly perturbed domains. It is somehow alternative to the more classical techniques of Asymptotic Analysis and, typically, it allows a representation of the solutions in terms of real analytic functions of the perturbation parameter. But there are problems for which we cannot expect real analyticity. For example, this is the case of a Poisson equation in a sector or cone domain with a perturbation pattern that approaches the vertex. We will see how the FAA can be modified to study these problems.
The results presented are part of a joint work with M. Costabel, M. Dauge, and P. Musolino.