Stability Theorems

  • Andrea Braides
Part of the Lecture Notes in Mathematics book series (LNM, volume 2094)


In this chapter we face the problem of determining conditions under which the minimizing-movement scheme commutes with Γ-convergence. Let \(F_{\varepsilon }\) Γ-converge to F with initial data \(x_{\varepsilon }\) converging to x 0. In Sect. 8.2 it is proved that by suitably choosing \(\varepsilon =\varepsilon (\tau )\) the minimizing movement along the sequence \(F_{\varepsilon }\) from \(x_{\varepsilon }\) converges to a minimizing movement for the limit F from x 0. A further issue is whether, by assuming some further properties on \(F_{\varepsilon }\) we may deduce that the same thing happens for any choice of \(\varepsilon\). In order to give an answer we will use results from the theory of gradient flows recently elaborated by Ambrosio, Gigli and Savaré, and by Sandier and Serfaty.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Andrea Braides
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma Tor VergataRomaItaly

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