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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang


IMPACT FACTOR 2018: 2.316

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1864-8266
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Volume 11, Issue 4

Issues

On the continuity of functionals defined on partitions

Matthias Ruf
  • Corresponding author
  • Zentrum Mathematik – M7, Technische Universität München, Boltzmannstr. 3,85748 Garching, München, Germany
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Published Online: 2017-04-19 | DOI: https://doi.org/10.1515/acv-2016-0061

Abstract

We characterize the continuity of prototypical functionals acting on finite Caccioppoli partitions and prove that it is equivalent to convergence of the perimeter of the jump set.

Keywords: Surface energies; continuity; finite partitions

MSC 2010: 28A75; 49Q15

References

  • [1]

    L. Ambrosio and A. Braides, Functionals defined on partitions of sets of finite perimeter II: Integral representation and Γ-convergence, J. Math. Pures. Appl. (9) 69 (1990), 285–305. Google Scholar

  • [2]

    L. Ambrosio and A. Braides, Functionals defined on partitions of sets of finite perimeter II: Semicontinuity, relaxation and homogenization, J. Math. Pures. Appl. (9) 69 (1990), 307–333. Google Scholar

  • [3]

    L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., Clarendon Press, New York, 2000. Google Scholar

  • [4]

    S. Baldo, Minimal interface criterion for phase transitions in mixtures of Cahn–Hilliard fluids, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), 67–90. CrossrefGoogle Scholar

  • [5]

    A. Braides and M. Cicalese, Interfaces, modulated phases and textures in lattice systems, Arch. Ration. Mech. Anal. 223 (2017), no. 2, 977–1017. Web of ScienceCrossrefGoogle Scholar

  • [6]

    A. Braides, S. Conti and A. Garroni, Density of polyhedral partitions, Calc. Var. Partial Differential Equations (2017), 10.1007/s00526-017-1108-x. Web of ScienceGoogle Scholar

  • [7]

    R. L. Jerrard and N. Jung, Strict convergence and minimal liftings in BV, Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), 1163–1176. Google Scholar

  • [8]

    Y. G. Reshetnyak, Weak convergence of completely additive vector functions on a set, Sib. Math. J. 9 (1968), 1039–1045. CrossrefGoogle Scholar

  • [9]

    F. Rindler and G. Shaw, Strictly continuous extension of functionals with linear growth to the space BV, Q. J. Math. 66 (2015), 953–978. Web of ScienceCrossrefGoogle Scholar

  • [10]

    D. Spector, Simple proofs of some results of Reshetnyak, Proc. Amer. Math. Soc. 139 (2011), 1681–1690. CrossrefWeb of ScienceGoogle Scholar

About the article


Received: 2016-12-12

Accepted: 2017-02-23

Published Online: 2017-04-19

Published in Print: 2018-10-01


Citation Information: Advances in Calculus of Variations, Volume 11, Issue 4, Pages 335–339, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2016-0061.

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