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.
13
411
430
L. Poggiolini; M. Spadini
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/649970
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