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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.

Information

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