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Quasiminima of degenerate functionals with non polynomial growth

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Si dimostra un teorema di regolarità per i quasiminimi di un funzionale degenere del tipo\(\int\limits_\Omega {b(x) A} (|Du|) dx\), conA(t) ad andamento non polinomiale eb(x) peos della classeA, di Muckenhoupt.

Summary

We prove a regularity theorem for quasiminima of a degenerate functional of the type\(\int\limits_\Omega {b(x) A} (|Du|) dx\), whereA (t) has non polynomial growth andb(x) is a weight belonging to theA, class of Muckenhoupt.

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References

  1. Attouch H., Sbordone C.,Asymptotic limits for perturbed functionals of Calculus of variations, Ricerche di Mat. 29 (1981), 85–124.

    MathSciNet  Google Scholar 

  2. Boccardo L., Marcellini P., Sbordone C.,L ∞-regularity for variational problems with sharp non standard growth conditions, Boll. Un. Mat. It. sez. A (7) 4-A (1990), 219–225.

    MathSciNet  Google Scholar 

  3. Chanillo S., Wheeden R. L.,Weighted Poincarè and Sobolev inequalities and estimates for weighted Peano maximal functions, American J. of Math. 107 (1985), 1191–1226.

    Article  MATH  MathSciNet  Google Scholar 

  4. Fabes E. B., Kenig C. E., Serapioni R.,The local regularity of solutions of degenerate elliptic equations, Comm. P.D.E. 7 (1982), 77–116.

    Article  MATH  MathSciNet  Google Scholar 

  5. Fiorenza A.,An inequality for Jensen means, J. Nonlinear Analysis T. M. A. 16, 2, (1991), 191–198.

    Article  MATH  MathSciNet  Google Scholar 

  6. Fusco N., Sbordone C.,Higher integrability from reverse Jensen inequalities with different supports, in P.D.E. and the Calculus of Variations vol. II, essays in Honor of Ennio De Giorgi, Birkhauser (1989), 541–562.

  7. Fusco N., Sbordone C.,Higher integrability of the gradient of minima of certain functionals, Rend. Acc. Sci. Fis. Mat. Napoli (1989).

  8. Fusco N., Sbordone C.,Higher integrability of the gradient of minimizers of functionals with non standard growth conditions, Comm. Pure Appl. Math. XLIII, (1990), 673–683.

    Article  MathSciNet  Google Scholar 

  9. Giaquinta M., Giusti E.,On the regularity of the minima of variational integrals, Acta Math. 148 (1982), 31–46.

    Article  MATH  MathSciNet  Google Scholar 

  10. Giaquinta M., Modica G.,Regularity results for some classes of higher order non linear elliptic systems, J. fur reine angew. Math. 311–312 (1979), 145–169.

    MathSciNet  Google Scholar 

  11. Giaquinta M.,Growth conditions and regularity. A counterexample, Manuscripta Math. 59, (1987) 245–248.

    Article  MATH  MathSciNet  Google Scholar 

  12. Marcellini P.,Un exemple de solution discontinue d'un probléme variationnelle dans le cas scalaire, J. Differential Equations (1990) (to appear).

  13. Marcellini P.,Regularity of minimizers of integrals of the Calculus of Variations with non standard growth conditions, Arch. Rational Mech. Analysis 105 (1989), 267–284.

    Article  MATH  MathSciNet  Google Scholar 

  14. Marcellini P.,Regularity and existence of solutions of elliptic equations with p-q growth conditions, Preprint Ist. Math. «U. Dini» Univ. Firenze 7 (1988).

  15. Modica G.,Quasiminimi di alcuni funzionali degeneri, Annali di Mat. Pura Appl. IV ser. 142 (1985), 121–143.

    Article  MATH  MathSciNet  Google Scholar 

  16. Moscariello G., Nania L.,Holder continuity of minimizers of functionals with non standard growth conditions (to appear on Ric. di Mat.).

  17. Shordone C.,Some reverse integral inequalities, Atti Accad. Pontaniana, Napoli vol., XXXII (1984), 1–15.

    Google Scholar 

  18. Sbordone C.,On some integral inequalities and their applications to the Calculus of Variations, Boll. Un. Mat. Ital. An. Funz. e Appl. serie VI vol 1 (1986), 73–94.

    MathSciNet  Google Scholar 

  19. Stroffolini B.,On some extensions of Hardy-Littlewood inequalities, Ricerche di Mat. XXXVIII, 1, (1989), 119–136.

    MathSciNet  Google Scholar 

  20. Wik I.,On Muckenhoupt's classes of weight functions, Studia Math. 94 (1989), 245–255.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni «R. Caccioppoli», dell'Università di Napoli, Via Mezzocannone 8, 80134, Napoli

    Carlo Sbordone

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  1. Carlo Sbordone
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(Conferenza tenuta il 13 novembre 1989)

This work has been performed as a part of a National Research Project, supported by MPI (40%, 1987).

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Sbordone, C. Quasiminima of degenerate functionals with non polynomial growth. Seminario Mat. e. Fis. di Milano 59, 173–184 (1989). https://doi.org/10.1007/BF02925300

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