Leoni, Giovanni:
On lower semicontinuity in the calculus of variations
Bollettino dell'Unione Matematica Italiana Serie 8 4-B (2001), fasc. n.2, p. 345-364, Unione Matematica Italiana (English)
pdf (521 Kb), djvu (264 Kb). | MR1831993 | Zbl 1072.49011
Sunto
Vengono studiate proprietà di semicontinuità per integrali multipli $$u\in W^{k, 1} (\Omega; \mathbb{R}^{d})\mapsto \int_{\Omega} f(x, u(x), \ldots \nabla^{k}u(x)) \, dx $$ quando $f$ soddisfa a condizioni di semicontinuità nelle variabili $(x, u, \ldots, \nabla^{k-1}u(x) )$ e può non essere soggetta a ipotesi di coercitività, e le successioni ammissibili in $W^{k, 1} (\Omega; \mathbb{R}^{d})$ convergono fortemente in $W^{k-1, 1} (\Omega; \mathbb{R}^{d})$.
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