We consider a general formulation of gradient flow evolution for problems whose natural framework is the one of metric spaces. The applications we deal with are concerned with the evolution of capacitary measures with respect to the -convergence dissipation distance and with the evolution of domains in spectral optimization problems.
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Dorin Bucur, Giuseppe Buttazzo, Ulisse Stefanelli, Shape flows for spectral optimization problems. Interfaces Free Bound. 14 (2012), no. 4, pp. 521–544