Geodesic
Degenerate Elliptic Equations and Morrey Spaces
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 989-1011 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{BUMI_2007_8_10B_3_a36,
     author = {Borrello, Francesco},
     title = {Degenerate {Elliptic} {Equations} and {Morrey} {Spaces}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {989--1011},
     year = {2007},
     volume = {Ser. 8, 10B},
     number = {3},
     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/