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manuscripta mathematica

, Volume 93, Issue 1, pp 283–299 | Cite as

Hölder continuity of minimizers of functionals with variable growth exponent

  • Valeria Chiadò Piat
  • Alessandra Coscia
Article

Keywords

Variable Exponent Compact Closure Standard Growth Condition Local Boundedness Caccioppoli Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    ACERBI E., FUSCO N.: Partial regularity under anisotropic (p, q) growth conditions.J. Diff. Equations. 107 (1994), 46–67.zbMATHCrossRefGoogle Scholar
  2. [2]
    ACERBI E., FUSCO N.: A transmission problem in the calculus of variations.Calc. Var. 2 (1994), 1–16.zbMATHCrossRefGoogle Scholar
  3. [3]
    ALKHUTOV YU. A.: The Hölder continuity of certain nonlinear elliptic equations with nonstandard growth condition.Differentsial’nye Uravneniya (1997) (to appear).Google Scholar
  4. [4]
    BOCCARDO, L., MARCELLINI, P., SBORDONE, C.: L∞-regularity for a variational problem with sharp non standard growth conditions.Boll. Un. Mat. Ital. (7)4-A (1990), 219–225.Google Scholar
  5. [5]
    BREZIS H.:Analyse fonctionnelle. Théorie et applications. Masson, Paris, 1983.zbMATHGoogle Scholar
  6. [6]
    DE GIORGI E.: Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari.Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 3 (1957), 25–43.Google Scholar
  7. [7]
    FAN X.: A class of De Giorgi type and Hölder continuity of minimizers of variationals withm(x)-growth condition. Preprint, Lanzhou University, China, 1995.Google Scholar
  8. [8]
    FUSCO N., SBORDONE C.: Local boundedness of minimizers in a limit case.Manuscripta Math. 69 (1990), 19–25.zbMATHCrossRefGoogle Scholar
  9. [9]
    FUSCO N., SBORDONE C.: Some remarks on the regularity of minima of anisotropic integrals.Comm. Partial Differential Equations 18 (1993), 154–167.CrossRefGoogle Scholar
  10. [10]
    GIAQUINTA M.: Growth conditions and regularity, a counterexample.Manuscripta Math. 59 (1987), 245–248.zbMATHCrossRefGoogle Scholar
  11. [11]
    GIAQUINTA M., GIUSTI E.: On the regularity of the minima of variational integrals.Acta Math. 148 (1982), 31–46.zbMATHCrossRefGoogle Scholar
  12. [12]
    GIAQUINTA M., GIUSTI E.: Quasi-minima.Ann. Inst. H. Poincaré, Analyse non linéaire.1 (1984), 79–107.zbMATHGoogle Scholar
  13. [13]
    GIUSTI E.:Metodi diretti nel calcolo delle variazioni. Pitagora, Bologna, 1994.zbMATHGoogle Scholar
  14. [14]
    HONG M. C.: Some remarks on the minimizers of variational integrals with non standard growth conditions.Boll. Un. Mat. Ital. (7)6-A (1992), 91–102.Google Scholar
  15. [15]
    LADYZHENSKAJA O. A., URAL’TSEVA N. N.:Equations aux dérivées partielles du type elliptique. Dunod, Paris, 1968.Google Scholar
  16. [16]
    MARCELLINI P.: Un exemple de solution discontinue d’un problème variationnel dans le cas scalaire.Preprint Univ. Florence, (1987).Google Scholar
  17. [17]
    MARCELLINI P.: Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions.Arch. Rational Mech. Anal. 105 (1989), 267–284.zbMATHCrossRefGoogle Scholar
  18. [18]
    MARCELLINI P.: Regularity and existence of solutions of elliptic equations withp,q-growth conditions.J. Diff. Equations. 90 (1991), 1–30.zbMATHCrossRefGoogle Scholar
  19. [19]
    MARCELLINI P.: Regularity for elliptic equations with general growth conditions.J. Diff. Equations. 105 (1993), 296–333.zbMATHCrossRefGoogle Scholar
  20. [20]
    MARCUS M., MIZEL V. J.: Absolute continuity on tracks and mappings of Sobolev Spaces.Arch. Rational Mech. Anal. 45 (1972), 294–320.zbMATHCrossRefGoogle Scholar
  21. [21]
    MASCOLO E., PAPI G.: Local boundedness of minimizers of integrals of the calculus of variations.Ann. Mat. Pura Appl. 167 (1994), 323–339.zbMATHCrossRefGoogle Scholar
  22. [22]
    MORREY C. B.:Multiple integrals in the calculus of variations. Springer, Berlin, 1968.Google Scholar
  23. [23]
    MOSCARIELLO G., NANIA L.: Hölder continuity of minimizers of functionals with non standard growth conditions.Ricerche Mat. XL (1991), 259–273.Google Scholar
  24. [24]
    ZHIKOV V. V.: Averaging of functionals of the calculus of variations and elasticity theory.Math. USSR Izvestiya.29 (1987), 33–66.CrossRefGoogle Scholar
  25. [25]
    ZHIKOV V. V.: Lavrentiev phenomenon and homogenization for some variational problems.Proc. Workshop “Composite media and homogenization theory”, Trieste, 1995.Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Valeria Chiadò Piat
    • 1
  • Alessandra Coscia
    • 2
  1. 1.Dip. di MatematicaPolitecnico di TorinoTorinoItaly
  2. 2.Dip. di MatematicaUniversità di ParmaParmaItaly

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