Estimates for domains of local invertibility of diffeomorphisms

Abstract

Using a novel Wintner-type formulation of the classical Peano's existence theorem [Math. Ann. 37 (1890), 182-228], we enhance Wazewski'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].