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Perturbation of non-linear partial differential variational inequalities, I†

Published online by Cambridge University Press:  14 February 2012

Elena Stroescu
Elena Stroescu
Affiliation:
Institute of Mathematics, Bucharest
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Synopsis

The present paper is devoted to the study of the weak respectively strong convergence of solutions of variational inequalities, with non-linear partial differential operators of the generalised divergence form and of monotone type, under a perturbation of the domain of the definition. In this study there are used convergence concepts defined according to [ 22] and abstract convergence theorems given in [15 and 16].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 1 , 1976 , pp. 1 - 12
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

1Agmon, S.. Lectures on elliptic boundary value problems (Princeton: Van Nostrand, 1965).Google Scholar
2Biroli, M.. Sulla approssimazione della soluzione di alcune diseguaglianze variazionali ellitiche non lineari. Instituto Lombardo Accad. Sci. Lett. Rend. A 103 (1969), 557–572.Google Scholar
3Brezis, H.. Equations et inequations nonlineaires dans les espaces vectoriels en dualite. Ann. Inst. Fourier (Grenoble) 18 (1968), 115–175.Google Scholar
4Browder, F. E.. Existence theorems for nonlinear partial differential equations. Global analysis (Proc. Sympos. Pure Math., 16, Berkeley Calif., 1968), 1-60 (Providence: Amer. Math. Soc., 1970).CrossRefGoogle Scholar
5Krasnoselskii, M.. Topological methods in the theory of non-linear integral equations (London: Pergamon, 1964).Google Scholar
6Leray, J. and Lions, J. L.. Quelques résultats de Visik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty-Browder. Bull. Soc. Math. France 93 (1965), 97–107.Google Scholar
7Lions, J. L. and Stampacchia, G.. Variational inequalities. Comm. Pure Appl. Math. 20 (1967), 493–519.Google Scholar
8Lions, J. L.. Quelques méthodes de resolution des problemes aux limites nonlineaires (Paris: Dunod, 1969).Google Scholar
9Mirgel, W.. Eine allgemeine Storungstheorie fur Variations-ungleichungen (Frankfurt Univ. Dissertation, 1971).Google Scholar
10Mosco, U.. Approximation of the solutions of some variational inequalities. Ann. Scuola Norm. Sup. Pisa 21 (1967), 373–394.Google Scholar
11Mosco, U.. Convergence of convex sets and of solutions of variational inequations. Advances in Math. 3 (1969), 510–585.CrossRefGoogle Scholar
12Mosco, U.. Perturbation of variational inequalities. (Nonlinear Functional Analysis. Proc. Sympos. Pure Math., 18, Chicago, III., 1968), 182–194 (Providence: Amer. Math. Soc, 1970).CrossRefGoogle Scholar
13Mosco, U.. An introduction to the approximate solution of variational inequalities. (Centro Internazionale Matematico Estivo, Erice, Constructive aspects of functional analysis, 1971) (Rome: Edizioni Cremonese, 1973).Google Scholar
14Sibony, M.. Sur 1 approximation d'équations et inéquations aux dériveés partielles nonlinéaires de type monotone. J. Math. Anal. Appl. 34(1971), 502–564.Google Scholar
15Stroescu, E.. Weak discrete convergence of solutions of variational inequalities. Rend. Mat. 8 (1975), 815–841.Google Scholar
16Stroescu, E. and Vivaldi, M. A.. Strong discrete convergence of solutions of variational inequalities, in press.Google Scholar
17Stroescu, E. and Vivaldi, M. A.. Convergenza discreta di vettori ed applicazioni, I (Universita degli studi di Roma, Instituto Matematico –Guido Castelnuovo, 1973).Google Scholar
18Stroescu, E.. Perturbation of nonlinear partial differential variational inequalities II, submitted for publication.Google Scholar
19Stummel, F.. Discrete Konvergenz linear Operatoren I. Math. Ann. 190 (1970), 45–92.CrossRefGoogle Scholar
20Stummel, F.. Discrete convergence of mapping. (Topics in numerical analysis. Proc. Roy. Irish. Acad. Conf. Numerical Analysis, University College Dublin, 1972), 285–310 (London: Academic, 1973).Google Scholar
21Stummel, F. and Reinhardt, J.. Discrete convergence of continuous mappings in metric spaces. Numerische insbesondere approximationstheoretische Behandlung von Funktionalgleichungen, Oberwolfach, 1972. Lecture Notes in Mathematics 333 (Berlin: Springer, 1973).Google Scholar
22Stummel, F.. Perturbation theory for Sobolev spaces. Proc. Roy. Soc. Edinburgh Sect. A 73 (1975), 5–49.CrossRefGoogle Scholar