Advertisement

Annali di Matematica Pura ed Applicata

, Volume 117, Issue 1, pp 297–310 | Cite as

Su talune disequazioni variazionali ellittiche non lineari del secondo ordine

  • Maria Erminia Marina Borghesani
Article

Summary

In this note, making use of a result of J. L. Lions, we examine some non linear elliptic variational inequalities defined on domains which may be unbounded. Such variational inequalities are associated to a uniformely second order elliptic operator. We start with the derivation of an existence theorem (on bounded domains) under non coerciveness assumptions. Next we examine the convergence for the solutions of a collection of variational inequalities. To this purpose we study convergence theorems for variational inequalities associated to operators belonging to a class of abstract mapping of pseudomonotone type between Banach spaces. The solvability of some variational inequalities on unbounded domains then follows directly.

Bibliografia

  1. [1]
    G. Bottaro,Alcune condizioni sufficienti per l'esistenza e l'unicità della soluzione di una disequazione variazionale non coerciva, Ann. Mat. Pura Appl., (4)106 (1975), pp. 187–209.CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    G. Bottaro -M. E. Marina,Problema di Dirichlet per equazioni ellittiche di tipo variazionale su insiemi non limitati, Boll. U.M.I., (4)8 (1973), pp. 46–56.MathSciNetGoogle Scholar
  3. [3]
    H. Brezis,Inequations variationnelles associées à des opérateurs d'évolution, N.A.T.O. School Venise (juin 1968), pp. 249–259.Google Scholar
  4. [3']
    H. Brezis -A. Haraux,Image d'une somme d'operateurs monotones et applications, Israel J. Math.,23 (1976), pp. 165–186.MathSciNetGoogle Scholar
  5. [4]
    F. E. Browder,Existence theorems for non-linear partial differential equations, Proc. Sympos. Pure Math.,16, American Math. Soc. (1970), pp. 1–60.Google Scholar
  6. [5]
    M. Chicco,Confronto fra due modi di definire le diseguaglianze per le funzioni di H 1 (Ω), Boll. U.M.I., (4)4 (1971), pp. 668–676.zbMATHMathSciNetGoogle Scholar
  7. [6]
    D. E. Edmunds - V. B. Moscatelli - J. R. Webb,Strongly non-linear elliptic operators in unbounded domains, Publ. Math. Bordeaux (1974), pp. 6–32.Google Scholar
  8. [7]
    P. Hess,Variational inequalities for strongly non-linear elliptic operators, J. Math. Pures et appl.,52 (1973), pp. 285–298.zbMATHMathSciNetGoogle Scholar
  9. [8]
    P. Hess,On a class of strongly non-linear elliptic variational inequalities, Math. Ann.,211 (1974), pp. 289–297.CrossRefzbMATHMathSciNetGoogle Scholar
  10. [9]
    P. Hess,On strongly nonlinear elliptic problems, Proc. conference in Analysis, Campinas (Brazil), 1974.Google Scholar
  11. [10]
    J. L. Lions,Quelques méthodes de resolution des problémes aux limites non linéaires, Dunod, Gauthier-Villars (1969).Google Scholar
  12. [11]
    M. E. Marina,Una disuguaglianza variazionale associata a un operatore ellittico che può degenerare e con condizioni al contorno di npo misto, Rend. Sem. Mat. Univ. Padova,54 (1976), pp. 107–121.zbMATHGoogle Scholar
  13. [12]
    U. Mosco,Convergence of convex sets and of solutions of variational inequalities, Advances in Mathematics (3),4 (1969), pp. 510–585.CrossRefMathSciNetGoogle Scholar
  14. [13]
    G. Stampacchia,Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinuous, Ann. Inst. Fourier, Grenoble,15 (1965), pp. 189–258.zbMATHMathSciNetGoogle Scholar
  15. [14]
    A. Torelli,Su un problema di filtrazione da un canale, Rend. Sem. Mat. Padova,52 (1974), pp. 25–58.MathSciNetGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1978

Authors and Affiliations

  • Maria Erminia Marina Borghesani
    • 1
  1. 1.Genova

Personalised recommendations