Geodesic
A Variational Principle for Gradient Flows of Nonconvex Energies
Journal of convex analysis, Tome 23 (2016) no. 1, pp. 53-75
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We present a variational approach to gradient flows of energies of the form E = ϕ1 - ϕ2 where ϕ1, ϕ2 are convex functionals on a Hilbert space. A global parameter-dependent functional over trajectories is proved to admit minimizers. These minimizers converge up to subsequences to gradient-flow trajectories as the parameter tends to zero. These results apply in particular to the case of non λ-convex energies E. The application of the abstract theory to classes of nonlinear parabolic equations with nonmonotone nonlinearities is presented.
Mots-clés : Evolution equations, gradient flow, nonconvex energy, variational formulation 
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     author = {G. Akagi and U. Stefanelli},
     title = {A {Variational} {Principle} for {Gradient} {Flows} of {Nonconvex} {Energies}},
     journal = {Journal of convex analysis},
     pages = {53--75},
     year = {2016},
     volume = {23},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2016_23_1_JCA_2016_23_1_a2/}
}
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G. Akagi; U. Stefanelli. A Variational Principle for Gradient Flows of Nonconvex Energies. Journal of convex analysis, Tome 23 (2016) no. 1, pp. 53-75. http://geodesic.mathdoc.fr/item/JCA_2016_23_1_JCA_2016_23_1_a2/