Generalizaciones del operador de Lamé-Navier en análisis de Clifford

Daniel Alfonso Santiesteban; Diego Esteban Gutierrez Valencia; Ricardo  Abreu Blaya; Yudier Peña Pérez

doi:10.22490/25394088.7583

Vol. 18 No. 1 (2024)

Published 2024-01-27

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Original article

Generalizations of the Lamé-Navier operator in Clifford analysis

DOI: https://doi.org/10.22490/25394088.7583

Daniel Alfonso Santiesteban Universidad Autónoma de Guerrero

Diego Esteban Gutierrez Valencia Universidad Autónoma de Guerrero

Ricardo Abreu Blaya Universidad Autónoma de Guerrero

Yudier Peña Pérez Universidad Autónoma de Guerrero

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Abstract
References

Clifford Analysis has helped to effectively interpret many of the equations of Mathematical
Physics, and in particular of the Mechanics of Continuous Media. In this paper we study a
natural generalization of the classical Lamé-Navier operator on Clifford algebras. The use of
Dirac operators constructed with arbitrary orthonormal bases leads to a great variety of
systems of partial differential equations of mathematical and physical interest. First, several
essential properties such as invariance over k-vector fields and ellipticity are studied. In
addition, a rewriting of the Lamé-Navier system in terms of the longitudinal and transverse
modules is presented. Finally, the Dirichlet problem associated with functions that cancel the
generalized Lamé-Navier operator is considered, and we determine the condition that causes
the ill-posedness of problem in the Hadamard sense.

keywords: Dirac operators, invariance, ellipticity, Lamé-Navier system, Dirichlet problem

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How to Cite

Alfonso Santiesteban, D., Gutierrez Valencia , D. E., Abreu Blaya, R. ., & Peña Pérez, Y. (2024). Generalizations of the Lamé-Navier operator in Clifford analysis. Publicaciones E Investigación, 18(1). https://doi.org/10.22490/25394088.7583

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