- Research Article
- Open access
- Published:
On the Sets of Regularity of Solutions for a Class of Degenerate Nonlinear Elliptic Fourth-Order Equations with Data
Boundary Value Problems volume 2007, Article number: 065825 (2007)
Abstract
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
Kovalevsky A, Nicolosi F: Existence of solutions of some degenerate nonlinear elliptic fourth-order equations with-data. Applicable Analysis 2002,81(4):905–914. 10.1080/0003681021000004492
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 2006,12(4):99–112.
Kovalevsky A, Nicolosi F: Existence and regularity of solutions to a system of degenerate nonlinear fourth-order equations. Nonlinear Analysis. Theory, Methods & Applications 2005,61(3):281–307. 10.1016/j.na.2004.07.044
Skrypnik IV: Higher order quasilinear elliptic equations with continuous generalized solutions. Differential Equations 1978,14(6):786–795.
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 2001,44(5):657–667. 10.1016/S0362-546X(99)00298-9
Skrypnik IV, Nicolosi F: On the regularity of solutions of higher-order degenerate nonlinear elliptic equations. Dopovīdī Natsīonal'noï Akademīï Nauk Ukraïni 1997, (3):24–28.
Kovalevsky A, Nicolosi F: On Hölder continuity of solutions of equations and variational inequalities with degenerate nonlinear elliptic high order operators. In Problemi Attuali dell'Analisi e della Fisica Matematica. Aracne Editrice, Rome, Italy; 2000:205–220.
Guglielmino F, Nicolosi F: -solutions of boundary value problems for degenerate elliptic operators. Ricerche di Matematica 1987,36(supplement):59–72.
Guglielmino F, Nicolosi F: Existence theorems for boundary value problems associated with quasilinear elliptic equations. Ricerche di Matematica 1988,37(1):157–176.
Lions J-L: Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires. Dunod, Paris, France; 1969:xx+554.
Skrypnik IV: Nonlinear Elliptic Equations of Higher Order. Naukova Dumka, Kiev, Ukraine; 1973.
Ladyzhenskaya OA, Ural'tseva NN: Linear and Quasilinear Elliptic Equations. Academic Press, New York, NY, USA; 1968:xviii+495.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Bonafede, S., Nicolosi, F. On the Sets of Regularity of Solutions for a Class of Degenerate Nonlinear Elliptic Fourth-Order Equations with Data. Bound Value Probl 2007, 065825 (2007). https://doi.org/10.1155/2007/65825
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/2007/65825