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On a class of nonlocal nonlinear elliptic problems


Chipot, M; Rodrigues, J (1992). On a class of nonlocal nonlinear elliptic problems. RAIRO Modelisation Mathematique et Analyse Numerique, 26(3):447-467.

Abstract

We give a direct approach to the solvability of a class of nonlocal problems which admit a formulation in terms of quasi- variational inequalities. We are motivated by nonlinear elliptic boundary value problems in which certain coefficients depend, in a rather general way, on the solution itself through global quantities like the total mass, the total flux or the total energy. We illustrate the existence results with several applications, including an implicit Signorini problem for steady diffusion of biological populations and a class of operator equations in nonlinear mechanics. We also discuss the non- uniqueness of the solutions.

We give a direct approach to the solvability of a class of nonlocal problems which admit a formulation in terms of quasi- variational inequalities. We are motivated by nonlinear elliptic boundary value problems in which certain coefficients depend, in a rather general way, on the solution itself through global quantities like the total mass, the total flux or the total energy. We illustrate the existence results with several applications, including an implicit Signorini problem for steady diffusion of biological populations and a class of operator equations in nonlinear mechanics. We also discuss the non- uniqueness of the solutions.

Citations

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:nonlocal problems; quasi-variational inequalities; nonlinear elliptic boundary value problems; existence; Signorini problem; steady diffusion of biological popoluations; nonlinear mechanics; non-uniqueness
Language:English
Date:1992
Deposited On:31 Aug 2010 08:45
Last Modified:05 Apr 2016 13:28
Publisher:Elsevier
ISSN:0764-583X
Free access at:Related URL. An embargo period may apply.
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1160135
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0765.35021
http://www.numdam.org/item?id=M2AN_1992__26_3_447_0

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