Second-Order Evolution Equations Associated with Convex Hamiltonians(1)
Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 81-94

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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.
Aubin, J. P.; Ekeland, I. Second-Order Evolution Equations Associated with Convex Hamiltonians(1). Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 81-94. doi: 10.4153/CMB-1980-011-x
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     author = {Aubin, J. P. and Ekeland, I.},
     title = {Second-Order {Evolution} {Equations} {Associated} with {Convex} {Hamiltonians(1)}},
     journal = {Canadian mathematical bulletin},
     pages = {81--94},
     year = {1980},
     volume = {23},
     number = {1},
     doi = {10.4153/CMB-1980-011-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-011-x/}
}
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