Skip to content


  • Research Article
  • Open Access

Bounds for elliptic operators in weighted spaces

Journal of Inequalities and Applications20062006:76215

  • Received: 24 November 2004
  • Accepted: 28 September 2005
  • Published:


Some estimates for solutions of the Dirichlet problem for second-order elliptic equations are obtained in this paper. Here the leading coefficients are locally VMO functions, while the hypotheses on the other coefficients and the boundary conditions involve a suitable weight function.


  • Boundary Condition
  • Weight Function
  • Elliptic Equation
  • Dirichlet Problem
  • Elliptic Operator


Authors’ Affiliations

Dipartimento di Matematica e Informatica, Facoltà di Scienze MM.FF.NN., Università di Salerno, Via Ponte don Melillo, Fisciano, SA, 84084, Italy


  1. Caso L, Cavaliere P, Transirico M: On the maximum principle for elliptic operators. Mathematical Inequalities & Applications 2004,7(3):405–418.MATHMathSciNetView ArticleGoogle Scholar
  2. Caso L, Transirico M: Some remarks on a class of weight functions. Commentationes Mathematicae Universitatis Carolinae 1996,37(3):469–477.MATHMathSciNetGoogle Scholar
  3. Chiarenza F, Frasca F, Longo P: -solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients. Transactions of the American Mathematical Society 1993,336(2):841–853. 10.2307/2154379MATHMathSciNetGoogle Scholar
  4. Pucci C: Limitazioni per soluzioni di equazioni ellittiche. Annali di Matematica Pura ed Applicata 1996, 74: 15–30.MathSciNetView ArticleGoogle Scholar
  5. Transirico M, Troisi M, Vitolo A: BMO spaces on domains of. Ricerche di Matematica 1996,45(2):355–378.MATHMathSciNetGoogle Scholar
  6. Troisi M: Su una classe di funzoni peso. Rendiconti. Accademia Nazionale delle Scienze detta dei XL. Serie V. Memorie di Matematica 1986,10(1):141–152.MATHMathSciNetGoogle Scholar
  7. Vitanza C: A new contribution to theregularity for a class of elliptic second order equations with discontinuous coefficients. Le Matematiche 1993,48(2):287–296.MATHMathSciNetGoogle Scholar
  8. Ziemer WP: Weakly Differentiable Functions, Graduate Texts in Mathematics. Volume 120. Springer, New York; 1989:xvi+308.View ArticleGoogle Scholar


© Loredana Caso 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.