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.
Felli, V., Siclari, G. (2022). Unique continuation from a crack's tip under Neumann boundary conditions. NONLINEAR ANALYSIS, 222(September 2022) [10.1016/j.na.2022.113002].
Unique continuation from a crack's tip under Neumann boundary conditions
Felli V.
;Siclari G.
2022
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.
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