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Second-Order Evolution Equations Associated with Convex Hamiltonians(1)

Published online by Cambridge University Press:  20 November 2018

J. P. Aubin  and
I. Ekeland
J. P. Aubin
Affiliation:
Centre de Recherches Mathematiques de la Decision Université Paris. Dauphine 75775 Paris Cedex 16, France
I. Ekeland
Affiliation:
Centre de Recherches Mathematiques de la Decision Université Paris. Dauphine 75775 Paris Cedex 16, France
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Many problems in mathematical physics can be formulated as differential equations of second order in time:

with V a convex functional. This is the Euler equation for the Lagrangian

which is convex with respect to x, and concave with respect to x.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 1 , 01 March 1980 , pp. 81 - 94
Copyright
Copyright © Canadian Mathematical Society 1980

Footnotes

(2)

J. P. Aubin, CEREMADE, University of Paris-Dauphine, 75775 Paris 16.

(3)

I. Ekeland, Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1W5 Canada; and CEREMADE, University of Paris-Dauphine.

(1)

Research supported by NRC Grants #67-9082 and 67-3990.

References

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3. Brezis, H. and Ekeland, I., Un principe variationnel associé à certaines équations paraboliques, Notes CRAS Paris t.282 (1976), pp. 971-974 and 1197-1198.Google Scholar
4. Brezis, M., Nirenberg, H., and Stampacchia, G., A remark on Ky Fan's minimax principle, Bol. Un. Mat. Ital. IV Ser. 6, 1972, pp. 293-300.Google Scholar
5. Ekeland, I. and Temam, R., Convex analysis and variational problems, North-Holland.Google Scholar
6. Fan, Ky, A minimax inequality and applications, Inequalities III, Shishia ?d., Academic Press (1972), pp. 103-113.Google Scholar
7. Schatzmann, M., Le système differentiel avec conditions initiales, Note CRAS Paris, t.284 (1976), pp. 603-606.Google Scholar