Open Access Research Article

On the Sets of Regularity of Solutions for a Class of Degenerate Nonlinear Elliptic Fourth-Order Equations with Data

S Bonafede1* and F Nicolosi2

Author Affiliations

1 Dipartimento di Economia dei Sistemi Agro-Forestali, Università delgi Studi di Palermo, Viale delle Scienze, Palermo 90128, Italy

2 Dipartimento di Matematica e Informatica, Università delgi Studi di Catania, Viale A. Doria 6, Catania 95125, Italy

For all author emails, please log on.

Boundary Value Problems 2007, 2007:065825 doi:10.1155/2007/65825


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/065825


Received:24 January 2007
Accepted:29 January 2007
Published:5 April 2007

© 2007 Bonafede and Nicolosi

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.

We establish Hölder continuity of generalized solutions of the Dirichlet problem, associated to a degenerate nonlinear fourth-order equation in an open bounded set , with data, on the subsets of where the behavior of weights and of the data is regular enough.

References

  1. Kovalevsky, A, Nicolosi, F: Existence of solutions of some degenerate nonlinear elliptic fourth-order equations with -data. Applicable Analysis. 81(4), 905–914 (2002). Publisher Full Text OpenURL

  2. Kovalevsky, A, Nicolosi, F: On the sets of boundedness of solutions for a class of degenerate nonlinear elliptic fourth-order equations with -data. Fundamentalnaya I Prikladnaya Matematika. 12(4), 99–112 (2006)

  3. Kovalevsky, A, Nicolosi, F: Existence and regularity of solutions to a system of degenerate nonlinear fourth-order equations. Nonlinear Analysis. Theory, Methods & Applications. 61(3), 281–307 (2005). PubMed Abstract | Publisher Full Text OpenURL

  4. Skrypnik, IV: Higher order quasilinear elliptic equations with continuous generalized solutions. Differential Equations. 14(6), 786–795 (1978)

  5. Bonafede, S, D'Asero, S: Hölder continuity of solutions for a class of nonlinear elliptic variational inequalities of high order. Nonlinear Analysis. Theory, Methods & Applications. 44(5), 657–667 (2001). PubMed Abstract | Publisher Full Text OpenURL

  6. Skrypnik, IV, Nicolosi, F: On the regularity of solutions of higher-order degenerate nonlinear elliptic equations. Dopovīdī Natsīonal'noï Akademīï Nauk Ukraïni.(3), 24–28 (1997). PubMed Abstract OpenURL

  7. Kovalevsky, A, Nicolosi, F: On Hölder continuity of solutions of equations and variational inequalities with degenerate nonlinear elliptic high order operators. Problemi Attuali dell'Analisi e della Fisica Matematica, pp. 205–220. Aracne Editrice, Rome, Italy (2000)

  8. Guglielmino, F, Nicolosi, F: -solutions of boundary value problems for degenerate elliptic operators. Ricerche di Matematica. 36(supplement), 59–72 (1987)

  9. Guglielmino, F, Nicolosi, F: Existence theorems for boundary value problems associated with quasilinear elliptic equations. Ricerche di Matematica. 37(1), 157–176 (1988)

  10. Lions, J-L: Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires,p. xx+554. Dunod, Paris, France (1969).

  11. Skrypnik, IV: Nonlinear Elliptic Equations of Higher Order, Naukova Dumka, Kiev, Ukraine (1973)

  12. Ladyzhenskaya, OA, Ural'tseva, NN: Linear and Quasilinear Elliptic Equations,p. xviii+495. Academic Press, New York, NY, USA (1968)