Estimates for domains of local invertibility of diffeomorphisms

Mustafa, Octavian; Rogovchenko, Yuri

doi:10.1090/S0002-9939-06-08444-9

Estimates for domains of local invertibility of diffeomorphisms
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by Octavian G. Mustafa and Yuri V. Rogovchenko PDF

Proc. Amer. Math. Soc. 135 (2007), 69-75 Request permission

Abstract:

Using a novel Wintner-type formulation of the classical Peano’s existence theorem [Math. Ann. 37 (1890), 182-228], we enhance Ważewski’s result on invertibility of maps defined on closed balls [Ann. Soc. Pol. Math. 20 (1947), 81-125] securing the size of the domain of invertibility that agrees with the bounds derived by John [Comm. Pure Appl. Math. 21 (1968), 77-110] and Sotomayor [Z. Angew. Math. Phys. 41 (1990), 306-310].

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