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On the boundary integral-equations for the crack opening displacement of flat cracks. (English) Zbl 0753.45005
The author considers the first kind boundary integral equations \(Du=f\) in a bounded smooth domain in the plane, where \(D\) is the hypersingular operator associated with the Helmholtz equation and the Lamé system, respectively. Regarding \(D\) is a pseudodifferential operator and computing its complete symbol, he proves a coerciveness estimate and a solvability result.

MSC:
45F15 Systems of singular linear integral equations
35C15 Integral representations of solutions to PDEs
47G30 Pseudodifferential operators
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
74R99 Fracture and damage
74J20 Wave scattering in solid mechanics
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