On the plane Lamé-Navier system in fractal domains

2020/05/15 by Valencia, Diego Esteban Gutierrez, Blaya, Ricardo Abreu, Alejandre, Martín Patricio Árciga +1
#30G35 (Primary) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.07827

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.

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