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Filippov Lemma for certain second order differential inclusions

Grzegorz Bartuzel, Andrzej Fryszkowski (2012)

Open Mathematics

In the paper we give an analogue of the Filippov Lemma for the second order differential inclusions with the initial conditions y(0) = 0, y′(0) = 0, where the matrix A ∈ ℝd×d and multifunction is Lipschitz continuous in y with a t-independent constant l. The main result is the following: Assume that F is measurable in t and integrably bounded. Let y 0 ∈ W 2,1 be an arbitrary function fulfilling the above initial conditions and such that where p 0 ∈ L 1[0, 1]. Then there exists a solution y ∈ W 2,1...

Funzioni ( p , q ) -convesse

Ennio De Giorgi, Antonio Marino, Mario Tosques (1982)

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

We study a class of functions which differ essentially from those which are the sum of a convex function and a regular one and which have interesting properties related to Γ -convergence and to problems with non-convex constraints. In particular some results are given for the associated evolution equations.

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