Skip to content

Advertisement

  • Research Article
  • Open Access

Bounds for elliptic operators in weighted spaces

Journal of Inequalities and Applications20062006:76215

https://doi.org/10.1155/JIA/2006/76215

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

Abstract

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.

Keywords

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

[12345678]

Authors’ Affiliations

(1)
Dipartimento di Matematica e Informatica, Facoltà di Scienze MM.FF.NN., Università di Salerno, Via Ponte don Melillo, Fisciano, SA, 84084, Italy

References

  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

Copyright

Advertisement