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On the Plane Lamé–Navier System in Fractal Domains

Abstract:

This paper is devoted to study a fundamental system of equations in plane Linear Elasticity Theory, the two-dimensional Lamé–Navier system. We rewrite them in a compressed form in terms of the Cauchy–Riemann operators and it allows us to solve a kind of Riemann problem for this system. A generalized Teodorescu operator, to be introduced here, provides the means for obtaining the explicit solution of this problem for a very wide classes of regions, including those with a fractal boundary.