Gradient flows of non convex functionals in Hilbert spaces and
 applications

Riccarda Rossi; Giuseppe Savaré

Displaying similar documents to “Gradient flows of non convex functionals in Hilbert spaces and applications”

Existence and approximation results for gradient flows

Riccarda Rossi, Giuseppe Savaré (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space $H$ $\{\begin{matrix} u^{'} (t) + \partial φ (u (t)) ∋ 0 a.e. in (0, T), \\ u (0) = u_{0}, \end{matrix}$ 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 $\partial φ$ is (a suitable limiting version of) its subdifferential. The interest for this kind of equations is motivated by a number of examples, which show that several mathematical models describing phase transitions phenomena and leading to systems of evolutionary...

A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems

Michael Ortiz, Alexander Mielke (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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This work is concerned with the reformulation of evolutionary problems in a weak form enabling consideration of solutions that may exhibit evolving microstructures. This reformulation is accomplished by expressing the evolutionary problem in variational form, i.e., by identifying a functional whose minimizers represent entire trajectories of the system. The particular class of functionals under consideration is derived by first defining a sequence of time-discretized minimum problems...

Continuous limits of discrete perimeters

Antonin Chambolle, Alessandro Giacomini, Luca Lussardi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula. These functionals, based on interactions, arise in discrete optimization and are known as a large class of problems which can be solved in polynomial time. In particular, some of them can be solved very efficiently by maximal flow algorithms and are quite popular in the image processing community. We study the limit in the continuum of these functionals, show that they always converge...

On the lower semicontinuous quasiconvex envelope for unbounded integrands (I)

Marcus Wagner (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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Motivated by the study of multidimensional control problems of Dieudonné-Rashevsky type, we raise the question how to understand to notion of quasiconvexity for a continuous function with a convex body K $\subset ℝ^{n m}$ instead of the whole space $ℝ^{n m}$ as the range of definition. In the present paper, we trace the consequences of an infinite extension of outside K, and thus study quasiconvex functions which are allowed to take the value +∞. As an appropriate envelope, we introduce and investigate the...