Existence and approximation results for gradient flows

Riccarda Rossi; Giuseppe Savaré

Gradient flows of non convex functionals in Hilbert spaces and applications

Riccarda Rossi, Giuseppe Savaré (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space $ℋ$ $\{\begin{matrix} u^{'} (t) + \partial_{ℓ} φ (u (t)) ∋ f (t) & a.e. in (0, T), u (0) = u_{0}, \end{matrix}$ where $φ : ℋ \to (- \infty, + \infty]$ is a proper, lower semicontinuous functional which is not supposed to be a (smooth perturbation of a) convex functional and $\partial_{ℓ} φ$ is (a suitable limiting version of) its subdifferential. We will present some new existence results for the solutions of the equation by exploiting a technique, featuring some ideas from the theory of and of . Our analysis is also motivated by...

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