When the plane is pie-sliced in $nleq 4$ parts (with nonempty interior and common vertex at the origin) our main result provides sufficient conditions for any map $L$, that is continuous and piecewise linear relatively to this slicing, to be invertible. This result cannot be plainly extended to a greater number of slices. Also, some examples show that the assumptions cannot be relaxed too much. Our result is proved by a combination of linear algebra and topological arguments.
Local inversion of planar maps with nice nondifferentiability structure / L. Poggiolini; M. Spadini. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - STAMPA. - 13:(2013), pp. 411-430. [10.1515/ans-2013-0209]
Local inversion of planar maps with nice nondifferentiability structure
POGGIOLINI, LAURA;SPADINI, MARCO
2013
Abstract
When the plane is pie-sliced in $nleq 4$ parts (with nonempty interior and common vertex at the origin) our main result provides sufficient conditions for any map $L$, that is continuous and piecewise linear relatively to this slicing, to be invertible. This result cannot be plainly extended to a greater number of slices. Also, some examples show that the assumptions cannot be relaxed too much. Our result is proved by a combination of linear algebra and topological arguments.File | Dimensione | Formato | |
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