Borrello: Degenerate Elliptic Equations and Morrey Spaces

Borrello, Francesco:
Degenerate Elliptic Equations and Morrey Spaces
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.3, p. 989-1011, Unione Matematica Italiana (English)
pdf (475 Kb), djvu (186 Kb). | MR 2507910 | Zbl 1184.35143

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In questo articolo viene studiata la regolarità locale per la soluzione generalizzata del problema di Dirichlet relativo all'equazione \begin{equation*} Lu \equiv X^*_i (a_{ij}X_ju)=f.\end{equation*} dove $X_1, X_2, \ldots, X_m$ sono campi vettoriali soddisfacenti la condizione di Hörmander e $a_{ij} \in L^{\infty}$. Viene data una formula di rappresentazione per la soluzione generalizzata in termini di funzione di Green. I risultati sono ottenuti grazie a opportune stime di quest'ultima. Nel caso in cui $f \geq 0$ i teoremi provati sono invertibili.

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Referenze Bibliografiche