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Two semilinear Dirichlet problems “almost” in duality

  • Lucio Boccardo
Article

Abstract

In this paper we study two semilinear Dirichlet problems; the linear parts (in some sense, in duality) are a problem with singular convection term and a problem with singular drift. The nonlinear lower order terms have a regularizing effect: the solutions of the corresponding linear problems are less regular.

References

  1. 1.
    Boccardo, L.: Problemi differenziali ellittici e parabolici con dati misure. Conferenza generale al Congresso UMI 1995. Boll. Unione Mat. Ital. 11–A, 439–461 (1997)Google Scholar
  2. 2.
    Boccardo, L.: Some developments on Dirichlet problems with discontinuous coefficients. Boll. Unione Mat. Ital. 2, 285–297 (2009)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Boccardo, L.: Dirichlet problems with singular convection terms and applications. J. Differ. Equ. 258, 2290–2314 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Boccardo, L.: Stampacchia-Calderon-Zygmund theory for linear elliptic equations with discontinuous coefficients and singular drift (preprint) Google Scholar
  5. 5.
    Boccardo, L., Diaz, J.I., Giachetti, D., Murat, F.: Existence of a solution for a weaker form of a nonlinear elliptic equation. Res. Notes Math. Ser. 208, 229–246 (1989). PitmanMathSciNetzbMATHGoogle Scholar
  6. 6.
    Boccardo, L., Gallouët, T.: Nonlinear elliptic equations with right hand side measures. Commun. P.D.E 17, 641–655 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Boccardo, L., Giachetti, D.: Existence results via regularity for some nonlinear elliptic problems. Commun. P.D.E 14, 663–680 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Bottaro, G., Marina, M.E.: Problema di Dirichlet per equazioni ellittiche di tipo variazionale su insiemi non limitati. Boll. Unione Mat. Ital. 8, 46–56 (1973)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Brezis, H., Strauss, W.A.: Semi-linear second-order elliptic equations in \(L^1\). J. Math. Soc. Jpn. 25, 565–590 (1973)CrossRefzbMATHGoogle Scholar
  10. 10.
    Cirmi, G.R.: Regularity of the solutions to nonlinear elliptic equations with a lower-order term. Nonlinear Anal. 25, 569–580 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Evans, L.C.: Partial Differential Equations. Amer. Math. Soc, Providence (1998)zbMATHGoogle Scholar
  12. 12.
    Leonori, T., Petitta, F.: Existence and regularity results for some singular elliptic problems. Adv. Nonlinear Stud. 7, 329–344 (2007)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Schaefer, H.H.: Uber die Methode der a priori-Schranken. Math. Ann. 129, 415–416 (1955)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Stampacchia, G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15, 189–258 (1965)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Unione Matematica Italiana 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma IRomeItaly

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