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. 
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     author = {Borrello, Francesco},
     title = {Degenerate {Elliptic} {Equations} and {Morrey} {Spaces}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {989--1011},
     publisher = {mathdoc},
     volume = {Ser. 8, 10B},
     number = {3},
     year = {2007},
     zbl = {1184.35143},
     mrnumber = {2507910},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a36/}
}
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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/