Leonetti, F. and Mascolo, E. and Siepe, F.:
Gradient regularity for minimizers of functionals under $p$-$q$ subquadratic growth
Bollettino dell'Unione Matematica Italiana Serie 8 4-B (2001), fasc. n.3, p. 571-586, Unione Matematica Italiana (English)
pdf (493 Kb), djvu (192 Kb). | MR1859423 | Zbl 1177.49057
Sunto
Si prova la maggior sommabilità del gradiente dei minimi locali di funzionali integrali della forma $$\int_{\Omega}f(Du) dx,$$ dove $f$ soddisfa l'ipotesi di crescita $$ |\xi|^{p}-c_{1}\leq f(\xi) \leq c( 1+|\xi|^{q}),$$ con $1 < p < q \leq 2$. L'integrando $f$ è $C^{2}$ e $DDf$ ha crescita $p-2$ dal basso e $q-2$ dall'alto.
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Con il contributo del Ministero per i Beni e le Attività Culturali