Revisiting Estimates for Domains of Invertibility of Diffeomorphisms View Full Text


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Article Info

DATE

2014-08-07

AUTHORS

Jinhai Chen, Hans Josef Pesch

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. More... »

PAGES

1-13

References to SciGraph publications

  • 1990-03. Inversion of smooth mappings in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 2012-04-28. Estimating Invertible Domains of Diffeomorphisms in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2000. Interior Point Methods: Current Status and Future Directions in HIGH PERFORMANCE OPTIMIZATION
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    http://scigraph.springernature.com/pub.10.1007/s10957-014-0632-5

    DOI

    http://dx.doi.org/10.1007/s10957-014-0632-5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1002811273


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