Auscher, P. and Qafsaoui, M.:
Observations on $W^{1,p}$ estimates for divergence elliptic equations with VMO coefficients
Bollettino dell'Unione Matematica Italiana Serie 8 5-B (2002), fasc. n.2, p. 487-509, Unione Matematica Italiana (English)
pdf (356 Kb), djvu (283 Kb). | MR1911202 | Zbl 1173.35419
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In questo lavoro esponiamo alcune osservazioni circa il lavoro di Di Fazio riguardante le stime $W^{1,p}$ per $1< p<\infty$ per soluzioni di equazioni ellittiche del tipo $\text{div} \, A \nabla u = \text{div} \, f$ su un dominio $\Omega$ con dati di Dirichlet nulli, $A$ nella classe $VMO$ ed $f$ in $L^{p}$. Si considera il caso in cui i coefficienti della parte principale sono complessi e la frontiera di $\Omega$ è di classe $C^{1}$. Si considera inoltre il caso del problema di Neumann non omogeneo e si dimostrano risultati analoghi. Il principale strumento utilizzato è una conveniente formula di rappresentazione per la funzione di Green e di Neumann.
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Con il contributo del Ministero per i Beni e le Attività Culturali