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Nella prima parte di questa Nota si dimostrano dei risultati di simmetria unidimensionale e radiale per le soluzioni di in . Questi risultati sono legati a due congetture (De Giorgi, 1978 e Gibbons, 1994) riguardanti la classificazione delle soluzioni dell’equazione in . Si dimostra, in particolare, la seguente generalizzazione della congettura di Gibbons: se e se l’insieme degli zeri di è limitato nella direzione , allora , ovvero, è unidimensionale. Nella seconda parte si considerano...
We describe the slopes, with respect to the coordinates hyperplanes, of the hypergeometric systems of codimension one, that is when the toric ideal is generated by one element.
In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians on the spheres . In the second part, we introduce a larger family of left-invariant sublaplacians on and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.
The (infinitesimal) symmetries of first and second-order partial differential equations represented by connections on fibered manifolds are studied within the framework of certain “strong horizontal“ structures closely related to the equations in question. The classification and global description of the symmetries is presented by means of some natural compatible structures, eġḃy vertical prolongations of connections.
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