Normal solvability of general linear elliptic problems.

Volpert, A.; Volpert, V.

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In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class $H_{0}^{1, p} (Ω)$ for all $1 < p < \infty$ and, as a consequence, the Hölder regularity of the solution $u$ . $ℒ$ is an elliptic second order operator with discontinuous coefficients $(V M O)$ and the lower order terms belong to suitable Lebesgue spaces.