Existence of minimizers and lower semicontinuity of integral functionals in the vectorial case

Silvia Bertirotti; Roberto Van der Putten

Displaying similar documents to “Existence of minimizers and lower semicontinuity of integral functionals in the vectorial case”

On lower semicontinuity in the calculus of variations

Giovanni Leoni (2001)

Bollettino dell'Unione Matematica Italiana

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Vengono studiate proprietà di semicontinuità per integrali multipli $u \in W^{k, 1} (Ω; R^{d}) \mapsto \int_{Ω} f (x, u (x), \dots \nabla^{k} u (x)) d x$ quando $f$ soddisfa a condizioni di semicontinuità nelle variabili $(x, u, \dots, \nabla^{k - 1} u (x))$ e può non essere soggetta a ipotesi di coercitività, e le successioni ammissibili in $W^{k, 1} (Ω; R^{d})$ convergono fortemente in $W^{k - 1, 1} (Ω; R^{d})$ .

Topological degree, Jacobian determinants and relaxation

Irene Fonseca, Nicola Fusco, Paolo Marcellini (2005)

Bollettino dell'Unione Matematica Italiana

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A characterization of the total variation $T V (u, Ω)$ of the Jacobian determinant $det D u$ is obtained for some classes of functions $u : Ω \to R^{n}$ outside the traditional regularity space $W^{1, n} (Ω; R^{n})$ . In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity $x_{0} \in Ω$ . Relations between $T V (u, Ω)$ and the distributional determinant $Det D u$ are established, and an integral representation is obtained for the relaxed energy of certain polyconvex functionals at maps $u \in W^{1, p} (Ω; R^{n}) \cap W^{1, \infty} (Ω \{x_{0}\}; R^{n})$ . ...

Lower semicontinuity of L∞ functionals

E. N. Barron, R. R. Jensen, C. Y. Wang (2001)

Annales de l'I.H.P. Analyse non linéaire

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Relaxation of elastic energies with free discontinuities and constraint on the strain

Andrea Braides, Anneliese Defranceschi, Enrico Vitali (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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As a model for the energy of a brittle elastic body we consider an integral functional consisting of two parts: a volume one (the usual linearly elastic energy) which is quadratic in the strain, and a surface part, which is concentrated along the fractures (i.e. on the discontinuities of the displacement function) and whose density depends on the jump part of the strain. We study the problem of the lower semicontinuous envelope of such a functional under the assumptions that the surface...

On the definition and the lower semicontinuity of certain quasiconvex integrals

Paolo Marcellini (1986)

Annales de l'I.H.P. Analyse non linéaire

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