Revisiting Estimates for Domains of Invertibility of Diffeomorphisms

Jinhai Chen () and Hans Josef Pesch ()
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Jinhai Chen: University of Rochester
Hans Josef Pesch: University of Bayreuth

Journal of Optimization Theory and Applications, 2015, vol. 165, issue 1, No 1, 13 pages

Abstract: Abstract This paper aims at revisiting estimates for domains of invertibility of diffeomorphisms. In contrast to previous results, we establish the estimates without the assumption of the underlying function being a diffeomorphism from its domain onto its range, and show that the arguments can be easily exploited to derive an analogous result in the framework of finite-dimensional spaces. Furthermore, the established results provide more estimates of the balls on which diffeomorphisms take place. In addition, we use these results to derive several variants of global inverse function theorem, which extend the known ones. The results presented in the paper are also applied to validate the existence of solutions for nonlinear equations.

Keywords: Diffeomorphism; Domain of invertibility; Continuation property; Existence of solutions; 46T20; 57R50; 47J05; 26B10; 26B05 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0632-5

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