Minimal regularity of the solutions of some transmission problems
Denis Mercier · Mathematical Methods in the Applied Sciences · 2003
Abstract We consider some transmission problems for the Laplace operator in two‐dimensional domains. Our goal is to give minimal regularity of the solutions, better than H1, with or without conditions on the (positive) material constants. Under a monotonicity or quasi‐monotonicity condition on the constants (or on the inverses according to the boundary conditions), we study the behaviour of the solution near vertex and near interior nodes and show in each case that the given regularity is sharp. Without condition we prove that the regularity near a corner is of the form H1+ρ, where ρ is a given bound depending on the material constants. Numerical examples are presented which confirm the sharpness of our lower bounds. Copyright © 2003 John Wiley & Sons, Ltd.