Hostname: page-component-5d59c44645-k78ct Total loading time: 0 Render date: 2024-02-21T11:59:56.865Z Has data issue: false hasContentIssue false

Problèmes elliptiques du 2ème ordre non sous forme divergence

Published online by Cambridge University Press:  14 November 2011

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


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.

Research Article
Copyright © Royal Society of Edinburgh 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



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), 623727.Google 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), 305352.Google Scholar
4Bony, J. M.. Principe du maximum dans les espaces de Sobolev. C.R. Acad. Sci. Paris Sér. A 265 (1967), 333336.Google Scholar
5Brezis, H.. Problèmes unilatéraux. J. Math. Pures Appl. 51 (1972), 1168.Google Scholar
6Chicco, M.. Sulle equazioni ellitiche del secondo ordine a coefficienti continui, Ann. Mat. Pura Appl. 88 (1971), 123133.Google 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), 374387.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), 10051015.Google 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), 345400 et 479–530.Google Scholar
12Troianiello, G. M.. Unilateral Dirichlet problems of the non-variational type. Ann. Mat. Pura Appl., à paraître.Google Scholar