Geodesic
Degenerate Elliptic Equations and Morrey Spaces
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 989-1011.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this paper we study local regularity for the generalized solution to the Dirichlet problem related to the equation \begin{equation*} Lu \equiv X^*_i (a_{ij}X_ju)=f. \end{equation*} where $X_{1}, X_2, \ldots, X_m$ are vector fields satisfying Hörmander condition and $a_{ij}\in L^\infty$. We give a representation formula for the generalized solution in terms of the Green function and thanks to suitable estimates we achieve our goal. In the case $f \geq 0$ we are able to give necessary condition too.
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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Borrello, Francesco. Degenerate Elliptic Equations and Morrey Spaces. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 989-1011. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a36/

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