Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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

CiteScore 2018: 1.77

SCImago Journal Rank (SJR) 2018: 2.350
Source Normalized Impact per Paper (SNIP) 2018: 1.465

Mathematical Citation Quotient (MCQ) 2018: 1.44

Online
ISSN
1864-8266
See all formats and pricing
More options …
Ahead of print

Issues

On the regularity of solutions to the plastoelasticity problem

Arrigo Cellina
  • Corresponding author
  • Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano, Italy
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-09-09 | DOI: https://doi.org/10.1515/acv-2017-0004

Abstract

We prove the local regularity of solutions to the problem of minimizing

Ω[L(v(x))+f(x)v(x)]𝑑xon u0+W01,(Ω),

where L is either 12|ξ|2 for |ξ|1 and + for |ξ|>1, or a more general convex, extended-valued function.

Keywords: Elasto-plasticity; regularity of solutions; variational problems

MSC 2010: 49K10; 49N60

References

  • [1]

    H. Brézis and D. Kinderlehrer, The smoothness of solutions to nonlinear variational inequalities, Indiana Univ. Math. J. 23 (1973/74), 831–844. Google Scholar

  • [2]

    H. Brézis and M. Sibony, Équivalence de deux inéquations variationnelles et applications, Arch. Ration. Mech. Anal. 41 (1971), 254–265. Google Scholar

  • [3]

    H. Brézis and G. Stampacchia, Sur la régularité de la solution d’inéquations elliptiques, Bull. Soc. Math. France 96 (1968), 153–180. Google Scholar

  • [4]

    L. A. Caffarelli and A. Friedman, The free boundary for elastic-plastic torsion problems, Trans. Amer. Math. Soc. 252 (1979), 65–97. CrossrefGoogle Scholar

  • [5]

    L. Esposito and G. Mingione, Some remarks on the regularity of weak solutions of degenerate elliptic systems, Rev. Mat. Complut. 11 (1998), no. 1, 203–219. Google Scholar

  • [6]

    J. Frehse, On the regularity of the solution of a second order variational inequality, Boll. Unione Mat. Ital. (4) 6 (1972), 312–315. Google Scholar

  • [7]

    C. Gerhardt, Regularity of solutions of nonlinear variational inequalities, Arch. Ration. Mech. Anal. 52 (1973), 389–393. CrossrefGoogle Scholar

  • [8]

    C. Gerhardt, Regularity of solutions of nonlinear variational inequalities with a gradient bound as constraint, Arch. Ration. Mech. Anal. 58 (1975), no. 4, 309–315. CrossrefGoogle Scholar

  • [9]

    P. Marcellini, Regularity for elliptic equations with general growth conditions, J. Differential Equations 105 (1993), no. 2, 296–333. CrossrefGoogle Scholar

  • [10]

    P. Marcellini, Everywhere regularity for a class of elliptic systems without growth conditions, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 23 (1996), no. 1, 1–25. Google Scholar

  • [11]

    G. A. Seregin, Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory, J. Math. Sci. (New York) 93 (1999), no. 5, 779–783. CrossrefGoogle Scholar

  • [12]

    T. W. Ting, Elastic-plasitc torsion of a square bar, Trans. Amer. Math. Soc. 123 (1966), 369–401. Google Scholar

About the article


Received: 2017-01-27

Revised: 2017-06-07

Accepted: 2017-06-12

Published Online: 2017-09-09


This work has been partially supported by INDAM-GNAMPA.


Citation Information: Advances in Calculus of Variations, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2017-0004.

Export Citation

© 2017 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Denis Bonheure, Francesca Colasuonno, and Juraj Földes
Annali di Matematica Pura ed Applicata (1923 -), 2018

Comments (0)

Please log in or register to comment.
Log in