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On the Lavrentieff phenomenon for some classes of Dirichlet minimum points.

De Arcangelis, Riccardo; Trombetti, Cristina — 2000

Journal of Convex Analysis

Rilassamento e fenomeno di Lavrentiev per alcune classi di funzionali integrali

Cristina Trombetti — 2000

Bollettino dell'Unione Matematica Italiana

A chain rule formula for the composition of a vector-valued function by a piecewise smooth function

François Murat; Cristina Trombetti — 2003

Bollettino dell'Unione Matematica Italiana

We state and prove a chain rule formula for the composition $T (u)$ of a vector-valued function $u \in W^{1, r} (Ω; R^{M})$ by a globally Lipschitz-continuous, piecewise $C^{1}$ function $T$ . We also prove that the map $u \to T (u)$ is continuous from $W^{1, r} (Ω; R^{M})$ into $W^{1, r} (Ω)$ for the strong topologies of these spaces.

Comparison results for Hessian equations via symmetrization

Barbara Brandolini; Cristina Trombetti — 2007

Journal of the European Mathematical Society

A quantitative version of the isoperimetric inequality : the anisotropic case

Luca Esposito; Nicola Fusco; Cristina Trombetti — 2005

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We state and prove a stability result for the anisotropic version of the isoperimetric inequality. Namely if $E$ is a set with small anisotropic isoperimetric deficit, then $E$ is “close” to the Wulff shape set.

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