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