Unique continuation from a crack's tip under Neumann boundary conditions. (September 2022)

• Record Type: Journal Article
• Authors: Felli, Veronica; Siclari, Giovanni
• Is Part Of: Nonlinear analysis. Volume 222(2022)
• Publication Date: 2022-09
• Subjects: 35C20 -- 35J25 -- 74A45; Crack singularities -- Monotonicity formula -- Unique continuation -- Blow-up analysis; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113002
• Languages: English
• ISSNs: 0362-546X

Abstract

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.