Unique continuation from a crack's tip under Neumann boundary conditions

2021/11/03 by Felli, Veronica, Siclari, Giovanni
#35C20 #35J25 #74A45 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.02379

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 a strong unique continuation principle.

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