Singular metrics and associated conformal groups underlying differential operators of mixed and degenerate types
Articolo
Data di Pubblicazione:
2006
Citazione:
Singular metrics and associated conformal groups underlying differential operators of mixed and degenerate types / K.R. Payne. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 185:4(2006), pp. 613-625.
Abstract:
For partial differential equations of mixed elliptic-hyperbolic and degenerate types which are the Euler-Lagrange equations for an
associated Lagrangian, we examine an associated metric structure which becomes singular on the hypersurface where the operator degenerates. In particular, we show that the ``non-trivial part'' of the complete symmetry group for the differential operator
(calculated in a previous paper by D. Lupo and K. R. Payne [Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types. Duke Math. J. (2005)]) corresponds to a group of local conformal transformations with respect to the metric away from the metric singularity and that the group extends smoothly across the singular surface. In this way, we define and calculate the conformal group for these operators as well as for lower order singular perturbations which are defined naturally by
the singular metric.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Conformal transformations; Lorentzian metrics; Mixed-type equations; Singular Riemannian; Symmetry groups
Elenco autori:
K.R. Payne
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