Jump problem for generalized Lam\'e-Navier systems in $\mathbb{R}^m$

Daniel Alfonso Santiesteban; Ricardo Abreu Blaya; Daniel Alpay

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arXiv · 2511.04959

Jump problem for generalized Lam\'e-Navier systems in $\mathbb{R}^m$

Daniel Alfonso Santiesteban·Ricardo Abreu Blaya·Daniel Alpay

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Abstract

This paper is devoted to study a fundamental system of equations in Linear Elasticity Theory: the famous Lam\'e-Navier system. The Clifford algebra language allows us to rewrite this system in terms of the Euclidean Dirac operator, which at the same time suggests a very natural generalization involving the so-called structural sets. Our interest lies mainly in the jump problem for these elastic systems. A generalized Teodorescu transform, to be introduced here, provides the means for obtaining the explicit solution of the jump problem for a very wide classes of regions, including those with a fractal boundary.

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Daniel Alfonso Santiesteban, Ricardo Abreu Blaya, Daniel Alpay. 2025-11-07. Jump problem for generalized Lam\'e-Navier systems in $\mathbb{R}^m$. https://arxiv.org/abs/2511.04959

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