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Regularizing effects of some lower order terms in non-uniformly nonlinear elliptic equations

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Abstract

We consider the Dirichlet problem for a class of strongly nonlinear elliptic equations with degenerate coercivity and data in divergence form. We show that some lower order terms have regularizing effects on solutions.

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References

  1. Alvino A., Boccardo L., Ferone V., Orsina L., Trombetti G.: Existence results for nonlinear elliptic equations with degenerate coercivity. Ann. Mat. Pura Appl. 182, 53–79 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alvino A., Ferone V., Trombetti G.: Nonlinear elliptic equations with lower-order terms. Differ. Integr. Equ. 14, 1169–1180 (2001)

    MATH  MathSciNet  Google Scholar 

  3. Alvino A., Ferone V., Trombetti G.: A priori estimates for a class of nonuniformly elliptic equations. Atti Semin. Mat. Fis. Univ. Modena. 46(suppl.), 381–391 (1998)

    MATH  MathSciNet  Google Scholar 

  4. Bénilan P., Boccardo L., Gallouët T., Gariepy R., Pierre M., Vazquez J.L.: An L 1-theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. IV. Ser. 22, 240–273 (1995)

    Google Scholar 

  5. Benkirane A., Youssfi A.: Regularity for solutions of nonlinear elliptic equations with degenerate coercivity. Ricerche Mat. 56(2), 241–275 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Benkirane A., Youssfi A., Meskine D.: Bounded solutions for nonlinear elliptic equations with degenerate coercivity and data in an LlogL. Bull. Belg. Math. Soc. Simon Stevin. 15(2), 369–375 (2008)

    MATH  MathSciNet  Google Scholar 

  7. Benkirane A., Youssfi A.: Existence of bounded solutions for a class of strongly nonlinear elliptic equations in Orlicz-Sobolev spaces. Aust. J. Math. Anal. Appl. 5(1), 1–26 (2008) Art. 7

    MathSciNet  Google Scholar 

  8. Boccardo L., Brézis H.: Some remarks on a class of elliptic equations with degenerate coercivity. Boll. Unione Mat. Ital. 6, 521–530 (2003)

    MATH  Google Scholar 

  9. Boccardo L., Dall’aglio A., Orsina L.: Existence and regularity results for some nonlinear equations with degenerate coercivity. Atti Sem. Mat. Fis. Univ. Modena 46(suppl.), 51–81 (1998)

    MATH  MathSciNet  Google Scholar 

  10. Boccardo, L., Gallouët, T., Murat, F.: A unified presentation of two existence results for problems with natural growth. In: Progress in PDE, the Metz surveys 2, 127–137 (1992) [M. Chipot editor, Pitman Res. Notes in Math. Ser., vol. 296. Longman Sci. Tech., Harlow (1993)]

  11. Boccardo L., Segurade Leon S., Trombetti C.: Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic gradient term. J. Math. Pures Appl. (9) 80, 919–940 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Brézis H., Browder F.E.: Some properties of higher order Sobolev spaces. J. Math. Pures Appl. 61, 245–259 (1982)

    MATH  MathSciNet  Google Scholar 

  13. Cirmi G.R.: Regularity of the solutions to nonlinear elliptic equations with a lower-order term. Nonlinear Anal. 25, 569–580 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  14. Croce G.: The regularizing effects of some lower order terms in an elliptic equation with degenerate coercivity. Rend. Mat. Appl. Serie VII 27, 299–314 (2007)

    MATH  MathSciNet  Google Scholar 

  15. Della Pietra F.: Existence results for non-uniformly elliptic equations with general growth in the gradient. Differ. Integr. Equ. 21, 821–836 (2008)

    MathSciNet  Google Scholar 

  16. Della Pietra, F.: Existence results for some classes of nonlinear elliptic problems. Dottorato thesis, Universit degli Studi di Napoli Federico II (2008)

  17. Kufner, A., John, O., Opic, B.: Function spaces. Academia, Praha (1977)

  18. Leray J., Lions J.L.: Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder. Bull. Soc. Mat. France. 93, 97–107 (1965)

    MATH  MathSciNet  Google Scholar 

  19. Stampacchia G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Ist. Fourier (Grenoble) 15, 189–258 (1965)

    MATH  MathSciNet  Google Scholar 

  20. Trombetti C.: Nonuniformly elliptic equations with natural growth in the gradient. Potent. Anal. 18, 391–404 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  21. Webb J.R.L.: Boundary value problems for strongly nonlinear elliptic equations. J. Lond. Math. Soc. 21, 123–132 (1980)

    Article  MATH  Google Scholar 

  22. Youssfi A.: Existence of bounded solutions for nonlinear degenerate elliptic equations in Orlicz spaces, Electron. J. Diff. Eqns. 2007(54), 1–13 (2007)

    MathSciNet  Google Scholar 

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Correspondence to Ahmed Youssfi.

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Benkirane, A., Youssfi, A. Regularizing effects of some lower order terms in non-uniformly nonlinear elliptic equations. Ricerche mat. 58, 185–205 (2009). https://doi.org/10.1007/s11587-009-0057-x

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