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Tytuł artykułu

Inverse Function Theorems and Jacobians over Metric Spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present inversion results for Lipschitz maps f : Ω ⊂ ℝN → (Y, d) and stability of inversion for uniformly convergent sequences. These results are based on the Area Formula and on the l.s.c. of metric Jacobians.
Wydawca
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2014-01-30
poprawiono
2014-04-28
zaakceptowano
2014-07-07
online
2014-07-26
Twórcy
  • Dipartimento di Matematica e Applicazioni, Università Federico II di Napoli, Via
    Cintia, Monte S. Angelo 80126 Napoli, Italy, luca.granieri@unina.it
Bibliografia
  • [1] E. Acerbi, G. Buttazzo, N. Fusco, Semicontinuity and Relaxation for Integrals Depending on Vector Valued Functions, J.Math.Pure et Appl. 62 (1983), 371-387.
  • [2] L. Ambrosio, B. Kircheim, Rectifiable sets in metric and Banach spaces, Math. Ann. 318 (3) (2000) 527–555.
  • [3] L. Ambrosio, B. Kircheim, Metric currents, Acta Mathematica 185 no. 1(2000), 1-80.
  • [4] L. Ambrosio, N. Fusco, D. Pallara, Function of Bounded Variations and Free Discontinbuity Problems,Oxford University Press,New York, 2000.
  • [5] L. Ambrosio, P. Tilli, Topics on Analysis in Metric Spaces, Oxford University Press, 2004.
  • [6] Erik Barvínek, Ivan Daler and Jan Franku, Convergence of sequences of inverse functions, Archivium Mathematicum, Vol.27 3-4 (1991), 201–204.
  • [7] Y. Benyamini, J. Lindenstrauss, Geometric Nonlinear Functional Analysis, Vol.1, AMS, 2000.
  • [8] Chung-Wu Ho, A note on proper maps, Proceedings AMS, Vol. 51 1 (1975), 237-241.
  • [9] P.G. Ciarlet, J. Necas, Injectivity and self-Contact in nonlinear elasticity, Arch. Rational Mech. Anal. 97 (1987), no. 3, 171-188.
  • [10] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer 2008.
  • [11] G. De Marco, G. Gorni, G. Zampieri, Global inversion of functions: an introduction, NODEA 1 (1994), 229-248.
  • [12] E. Durand-Cartagena, J.A. Jaramillo, Pointwise Lipschitz functions on metric spaces, J. Math. Anal. Appl. 363 (2010), 525–548.
  • [13] I. Fonseca, W. Gangbo, Degree Theory in Analysis and Applications, Clarendom Press Oxford, 1995.
  • [14] W. Fulton, Algebraic Topology, Springer, 1995.
  • [15] J. Gevirtz, Metric conditions that imply local invertibility, Communications in Pure and AppliedMathematics 23 (1969), 243–264.
  • [16] J. Gevirtz, Injectvity in Banach spaces and the Mazur-Ulam Theorem on Isometries, Transactions AMS 274, no. 1 (1982),307–318.
  • [17] J. Gevirtz, A sharp condition for univalence in Euclidean spaces, Proceedings AMS 57, no. 2 (1976), 261–265.
  • [18] L. Granieri, Metric currents and geometry of Wasserstein spaces, Rend. Semin. Mat. Univ. Padova 124 (2010), 91-125.
  • [19] L. Granieri, F. Maddalena, A metric approach to elastic reformations, Acta Mathematica Applicandae, published online December2013.
  • [20] L. Granieri, G. Mola, Sequences of inverse and implicit functions, in preparation.
  • [21] C. Gutierrez, C. Biasi, Finite Branched Coverings in a Generalized Inverse Mapping Theorem, Int. Journal of Math. Analysis2 no. 4 (2008), 169–179.
  • [22] F. John, On Quasi-Isometric Mappings I, Communications in Pure and Applied Mathematics 21 (1968), 77–110.
  • [23] M. B. Karmanova, Area and Coarea Formulas for the mappings of Sobolev classes with values in a metric space, SiberianMathematical Journal, Vol. 48, No. 4 (2007), 621–628. Proceedings of the AmericanMathematical Society, 121, No. 1 (1994),113–123.[WoS]
  • [24] B. Kirchheim, Rectifiable Metric Spaces: Local Structure and Regularity of the Hausdorff Measure, Proceedings of the AmericanMathematical Society, 121, No. 1 (1994), 113–123.
  • [25] L. V. Kovalev, Jani Onninen, On invertibility of Sobolev mappings, Journal für die reine und angewandte Mathematik, 656,(2011), 1–16.
  • [26] L. V. Kovalev, Jani Onninen, Kai Rajala, Invertibility of Sobolev mappings under minimal hypotheses, Ann. Inst. H. PoincaréAnal. Non Linéaire 27 (2010), no. 2, 517–528.
  • [27] A. Lytchak, Open map Theorem for metric spaces, St. Petersburg Math. J. 17 (2006), No. 3, 477–491.
  • [28] V. Magnani, An Area formula in metric spaces, Colloq. Math. 124 (2011), no. 2, 275-283.
  • [29] J. S. Raymond, Local inversion for differentiable functions and Darboux property, Mathematika 49 (2002), no. 1-2, 141-158.[Crossref]
  • [30] Yu. G. Reshetnyak, Space Mappings with Bounded Distortion, AMS, 1989.
  • [31] O. Martio, S. Rickman and J. Vaisala, Topological and Metric Properties of Quasiregular Mappings, Annales Academie ScientiarumFennicae Mathematica, 488 (1971), 1–31.
  • [32] M. Seeotharama Gowda, R. Sznajder, Weak connectedness of inverse images of continuus functions, Mathematics of OperationsReaserch 24 (1999), No. 1, 255-261.
  • [33] R. Van Der Putten, A note on the local invertibility of Sobolev functions, Math. Scand. 83 (1998), 255–264.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_agms-2014-0008
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