Geodesic
Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 651-663.

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In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class $H^{1,p}_0(\Omega)$ for all $1$ and, as a consequence, the Hölder regularity of the solution $u$. $\Cal L$ is an elliptic second order operator with discontinuous coefficients $(VMO)$ and the lower order terms belong to suitable Lebesgue spaces.
Classification : 35B65, 35J15, 35J30, 35R05, 45P05, 46E35, 46N20
Keywords: elliptic equations; Morrey spaces 
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     title = {Elliptic boundary value problem in {Vanishing} {Mean} {Oscillation} hypothesis},
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Ragusa, Maria Alessandra. Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 4, pp. 651-663. http://geodesic.mathdoc.fr/item/CMUC_1999__40_4_a4/