Generalizaciones del operador de Lamé-Navier en análisis de clifford.

Abstract

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 LaméNavier operator is considered, and we determine the condition that causes the ill-posedness of problem in the Hadamard sense.