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Annali di Matematica Pura ed Applicata

, Volume 159, Issue 1, pp 117–131 | Cite as

On a class of singular nonlinear parabolic variational inequalities

  • Marco Luigi Bernardi
  • Gianni Arrigo Pozzi
Article

Summary

We study a class of singular or degenerate parabolic variational inequalities, containing some nonlinear operators. We prove an existence and uniqueness result for weak solutions, in the framework of suitable Banach weighted spaces.

Keywords

Weak Solution Variational Inequality Nonlinear Operator Weighted Space Parabolic Variational Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Sunto

Si studia una classe di disequazioni variazionali paraboliche singolari o degeneri, contenenti operatori non lineari. Si dimostra un risultato di esistenza e unicità per soluzioni deboli, nell'ambito di opportuni spazi di Banach con peso.

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References

  1. [1]
    E. Asplund,Averaged norms, Israel J. Math.,5 (1967), pp. 227–233.Google Scholar
  2. [2]
    C. Baiocchi -M. S. Baouendi,Singular evolution equations, J. Funct. Anal.,25 (1977), pp. 103–120.Google Scholar
  3. [3]
    M. L. Bernardi,Su alcune equazioni d'evoluzione singolari, Boll. Un. Mat. Ital., (5),13-B (1976), pp. 498–517.Google Scholar
  4. [4]
    M. L. Bernardi,On some singular nonlinear evolution equations, Proc. Conf. on Diff. Equations in Banach Spaces (ed. by A. Favini and E. Obrecht),Lecture Notes in Math., Springer, Vol. 1223 (1986), pp. 12–24.Google Scholar
  5. [5]
    M. L. Bernardi -G. A. Pozzi,On some singular or degenerate parabolic variational inequalities, Houston J. Math.,15 (1989), pp. 163–192.Google Scholar
  6. [6]
    G. Da Prato -P. Grisvard,On an abstract singular Cauchy problem, Comm. in P.D.E.,3 (1978), pp. 1077–1082.Google Scholar
  7. [7]
    G. Dore -A. Venni,On a singular evolution equation in Banach spaces, J. Funct. Anal.,64 (1985), pp. 227–250.Google Scholar
  8. [8]
    A. Favini,Degenerate and singular evolution equations in Banach spaces, Math. Annalen,273 (1985), pp. 17–44.Google Scholar
  9. [9]
    G. H. Hardy -J. E. Littlewood -G. Polya,Inequalities, University Press, Cambridge, 1952.Google Scholar
  10. [10]
    J. E. Lewis -C. Parenti,Abstract singular parabolic equations, Comm. in P.D.E.,7 (1982), pp. 279–324.Google Scholar
  11. [11]
    J. L. Lions,Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod-Gauthier Villars, Paris, 1969.Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1991

Authors and Affiliations

  • Marco Luigi Bernardi
    • 1
  • Gianni Arrigo Pozzi
    • 2
  1. 1.Dipartimento di Automazione IndustrialeUniversità degli Studi di BresciaBresciaItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di PaviaPaviaItaly

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