Diffeomorphisms of $\Bbb R^n$ with oscillatory jacobians

• Autores: Nelson M. Kuhl, Waldyr M. Oliva, Luiz T. Magalhaes
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 37, Nº 2, 1993, págs. 255-269
• Idioma: inglés
• DOI: 10.5565/publmat_37293_02
• Títulos paralelos:
  • Difeomorfismos de Rn con jacobianos oscilatorios
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• Resumen

  • The paper presents, mainly, two results: a new proof of the spectral properties of oscillatory matrices and a transversality theorem for diffeomorphisms of Rn with oscillatory jacobian at every point and such that NM(f(x) - f(y)) = NM(x - y) for all elements x,y Î Rn, where NM(x) - 1 denotes the maximum number of sign changes in the components zi of z Î Rn, where all zi are non zero and z varies in a small neighborhood of x. An application to a semiimplicit discretization of the scalar heat equation with Dirichlet boundary conditions is also made.