Annali di Matematica Pura ed Applicata

, Volume 178, Issue 1, pp 325–338 | Cite as

Dirichlet problem for a divergence form elliptic equation with unbounded coefficients in an unbounded domain

  • Maurizio Chicco
  • Marina Venturino
Article

Abstract

We prove existence and uniqueness of the solution of the Dirichlet problem for a class of elliptic equations in divergence form with discontinuous and unbounded coefficients in unbounded domains.

Keywords

Unique Solution Elliptic Equation Bilinear Form Dirichlet Problem Sobolev Inequality 
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References

  1. [1]
    H. Brézis,Analyse fonctionnelle, théorie et applications, Masson, Paris, 1992.MATHGoogle Scholar
  2. [2]
    M. Chicco—M. Venturino,A priori inequalities in L ∞ (Ω) for solutions of elliptic equations in unbounded domains, Rend. Sem. Mat. Univ. Padova,102 (1999), pp. 141–149.MATHMathSciNetGoogle Scholar
  3. [3]
    E. Gagliardo,Proprietà di alcune classi di funzioni in più variabili, Ricerche Mat.,7 (1958), pp. 102–137.MATHMathSciNetGoogle Scholar
  4. [4]
    P. L. Lions,Remarques sur les équations linéaires elliptiques du second ordre sous forme divergence dans les domaines non bornés, Atti Acc. Naz. Lincei Rend. Sc. Fis. Mat. Natur., (8),78 (1985), pp. 205–212.MATHGoogle Scholar
  5. [5]
    P. L. Lions,Remarques sur les équations linéaires elliptiques du second ordre sous forme divergence dans les domaines non bornés, II, Atti Acc. Naz. Lincei Rend. Sc. Fis. Mat. Natur. (8),79 (1985), pp. 178–183.MATHGoogle Scholar
  6. [6]
    C. Miranda,Alcune osservazioni sulla maggiorazione in L ν delle soluzioni delle equazioni ellittiche del secondo ordine, Ann. Mat. Pura Appl. (4),61 (1963), pp. 151–170.MATHMathSciNetGoogle Scholar
  7. [7]
    G. Stampacchia,Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier, Grenoble,15 (1965), pp. 189–258.MATHMathSciNetGoogle Scholar
  8. [8]
    G. Talenti,Best constant in Sobolev inequality, Ann. Mat. Pura Appl. (4),110 (1976), pp. 353–372.MATHMathSciNetGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Pure ed Applicata 2000

Authors and Affiliations

  • Maurizio Chicco
    • 1
  • Marina Venturino
    • 1
  1. 1.Dipartimento di Metodi e Modelli MatematiciUniversità di GenovaGenovaItalia

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