## Maria Alessandra Ragusa

*Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis *

Comment.Math.Univ.Carolinae 40,4 (1999) 651-663. **Abstract:**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<p<\infty $ and, as a consequence, the H\"older regularity of the solution $u$. \par $\Cal L$ is an elliptic second order operator with discontinuous coefficients $(VMO)$ and the lower order terms belong to suitable Lebesgue spaces.

**Keywords:** elliptic equations, Morrey spaces

**AMS Subject Classification:** Primary 46E35, 35R05, 45P05; Secondary 35B65, 35J15

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