Unique continuation from a crack's tip under Neumann boundary conditions. (September 2022) - Felli, Veronica; Siclari, Giovanni
Abstract: We derive local asymptotics of solutions to second order elliptic equations at the edge of a ( N − 1 ) -dimensional crack, with homogeneous Neumann boundary conditions prescribed on both sides of the crack. A combination of blow-up analysis and monotonicity arguments provides a classification of all possible asymptotic homogeneities of solutions at the crack's tip, together with a strong unique continuation principle.