Regularity results of Stokes/Lamé interface problems
Denis Mercier, Serge Nicaise · Mathematische Nachrichten · 2011
Abstract This paper is devoted to some transmission problems involving the Lamé and stationary Stokes systems in two‐dimensional nonsmooth domains. We first show that these problems may be obtained as a limit of a transmission Lamé problem when the Lamé coefficient λ goes to infinity. We further investigate the behavior of the solutions of these problems near geometrical singularities, especially near corner points where the interface intersects the boundaries. In particular we show stable decompositions with respect to the perturbation parameter λ. Some minimal regularity results are deduced from similar minimal regularity result of transmission Lamé problems obtained in 13 . Some numerical results for the calculation of the singular exponents in the asymptotic expansion are presented and confirm these minimal regularity results.