Revisiting Estimates for Domains of Invertibility of Diffeomorphisms

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• 作者：Jinhai Chen (1)
  Hans Josef Pesch (2)
  
  1. University of Rochester ; Rochester ; NY ; 14642 ; USA
  2. University of Bayreuth ; 95440 ; Bayreuth ; Germany
  
• 关键词：Diffeomorphism ; Domain of invertibility ; Continuation property ; Existence of solutions ; 46T20 ; 57R50 ; 47J05 ; 26B10 ; 26B05
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：165
• 期：1
• 页码：1-13
• 全文大小：182 KB
• 参考文献：1. Rheinboldt, WC (1969) Local mapping relations and global implicit function theorems. Trans. Am. Math. Soc. 138: pp. 183-198 CrossRef
  2. Ortega, JM, Rheinboldt, WC (1970) Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York
  3. Plastock, R (1974) Homeomorphisms between Banach spaces. Trans. Am. Math. Soc. 200: pp. 169-183 CrossRef
  4. Chen, J (2012) Estimating invertible domains of diffeomorphisms. J. Optim. Theory Appl. 154: pp. 818-829 CrossRef
  5. Mustafa, OG, Rogovchenko, YV (2007) Estimates for domains of local invertibility of diffeomorphisms. Proc. Am. Math. Soc. 135: pp. 69-75 CrossRef
  6. Sotomayor, J (1990) Inversion of smooth mappings. Z. Angew. Math. Phys. 41: pp. 306-310 CrossRef
  7. Cristea, M (1981) A note on global inversion theorems and applications to differential equations. Nonlinear Anal. 5: pp. 1155-1161 CrossRef
  8. R膬dulescu, M, R膬dulescu, S (1980) Global inversion theorems and applications to differential equations. Nonlinear Anal. 4: pp. 951-965 CrossRef
  9. R膬dulescu, M, R膬dulescu, S (1989) Local inversion theorems without assuming continuous differentiability. J. Math. Anal. Appl. 138: pp. 581-590 CrossRef
  10. Freund, RM, Mizuno, S Interior point methods: current status and future directions. In: Frenk, H eds. (2000) High Performance Optimization. Kluwer Acad. Publ., Dordrecht, pp. 441-466 CrossRef
  
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878

文摘

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.