Norm-Resolvent Convergence in Perforated Domains

For several different types of boundary conditions (Dirichlet, Neumann and Robin), we prove norm-resolvent convergence in L2 for the Laplacian in an open domain perforated epsilon-periodically by spherical holes. The limit operator is of the form -Δ+m on the unperforated domain, where m is a positive constant.
This is an improvement of previous results [Cioranescu & Murat. A Strange Term Coming From Nowhere, Progress in Nonlinear Differential Equations and Their Applications, 31, (1997)], [S. Kaizu. The Robin Problems on Domains with Many Tiny Holes. Proc. Japan Acad., 61, Ser. A (1985)], which show strong resolvent convergence.
In particular, our result implies convergence of the spectrum of the operator for the perforated domain problem.

• Speaker: Frank Roesler (Cardiff University)
• Thursday 22 November 2018, 15:00–16:00
• Venue: MR14, Centre for Mathematical Sciences.
• Series: Applied and Computational Analysis; organiser: Dr Hansen.