Gamma-convergence of gradient flows on Hilbert and metric spaces and applications

@inproceedings{Serfaty2010GammaconvergenceOG,
  title={Gamma-convergence of gradient flows on Hilbert and metric spaces and applications},
  author={Sylvia Serfaty},
  year={2010}
}
We are concerned with Γ-convergence of gradient flows, which is a notion meant to ensure that if a family of energy functionals depending of a parameter Γ-converges, then the solutions to the associated gradient flows converge as well. In this paper we present both a review of the abstract “theory” and of the applications it has had, and a generalization of the scheme to metric spaces which has not appeared elsewhere. We also mention open problems and perspectives. Γ-convergence was introduced… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 47 references

Gradient flows in metric spaces and in the space of probability measures

L. Ambrosio, N. Gigli, G. Savaré
Lectures in Mathematics ETH Zürich. Birkhäuser • 2008
View 7 Excerpts
Highly Influenced

Vortices in the Magnetic Ginzburg-Landau Model

E. Sandier, S. Serfaty
Progress in Nonlinear Differential Equations and their Applications, vol 70, Birkhauser • 2007
View 3 Excerpts
Highly Influenced

Optimal transport

C. Villani
Old and new, Springer • 2009
View 1 Excerpt

A Simple Proof of Convergence of the Allen-Cahn Equation to Brakke’s Motion by Mean Curvature

N. Sato
Indiana Univ. Math. J, • 2008

Weak convergence methods for Hamiltonian multiscale problems

A. Mielke
DCDS(A) Discrete Contin. Dyn. Syst. Ser. A, • 2008

Γ-limits and relaxations for rate-independent evolutionary problems

MRS A. Mielke, T. Roubicek, U. Stefanelli
Calc. Var. PDE, • 2008

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