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Problèmes elliptiques du 2ème ordre non sous forme divergence

Published online by Cambridge University Press:  14 November 2011

Pierre-Louis Lions
Pierre-Louis Lions
Affiliation:
Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, 5 Place Jussieu, Paris
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Synopsis

We prove existence and uniqueness results for the solution of nonlinear elliptic boundary value problems, where the linear part of the equation is given by a second-order elliptic operator not in divergence form.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 3-4 , 1979 , pp. 263 - 271
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

Bibliographie

1Agmon, S., Douglis, A. et Nirenberg, L.. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Comm. Pure Appl. Math. 12 (1959), 623–727.CrossRefGoogle Scholar
2Agmon, S.. Lectures on elliptic boundary value problems (New York: Van Nostrand, 1965).Google Scholar
3Bensoussan, A. et Friedman, A.. Nonlinear variational inequalities and differential games with stopping times. J. Functional Analysis 16 (1974), 305–352.CrossRefGoogle Scholar
4Bony, J. M.. Principe du maximum dans les espaces de Sobolev. C.R. Acad. Sci. Paris Sér. A 265 (1967), 333–336.Google Scholar
5Brezis, H.. Problèmes unilatéraux. J. Math. Pures Appl. 51 (1972), 1–168.Google Scholar
6Chicco, M.. Sulle equazioni ellitiche del secondo ordine a coefficienti continui, Ann. Mat. Pura Appl. 88 (1971), 123–133.CrossRefGoogle Scholar
7Chicco, M.. Solvability of the Dirichlet problem in H 2.p(Ω) for a class of linear second-order elliptic equations. Boll. Un. Mat. Ital. 4 (1971), 374–387.Google Scholar
8Friedman, A.. The asymptotic behavior of the first real eigenvalue of a second-order elliptic operator with a small parameter in the highest derivatives. Indiana Univ. Math. J. 22 (1973), 1005–1015.CrossRefGoogle Scholar
9Hanouzet, B. et Joly, J. L.. Méthodes d'ordre dans l'interprétation de certaines inéquations variationnelles et applications, à paraître.Google Scholar
10Lions, P. L.. Une remarque sur des problémes elliptiques non coercifs Boll. Un. Mat. Ital., à paraître.Google Scholar
11Stroock, D. W. et Varadhan, S. R. S.. Diffusion processes with continuous coefficients I and II. Comm. Pure Appl. Math. 22 (1969), 345–400 et 479–530.CrossRefGoogle Scholar
12Troianiello, G. M.. Unilateral Dirichlet problems of the non-variational type. Ann. Mat. Pura Appl., à paraître.Google Scholar