The connections between Dirichlet, regularity and Neumann problems for second order elliptic operators with complex bounded measurable coefficients
The author shows that for general elliptic operators with complex bounded measurable coefficients, the solvability of the regularity problem does not imply the solvability of the dual Dirichlet problem, contrarily to the result by \textit{C. E. Kenig} and \textit{J. Pipher} [Invent. Math. 113, No. 3, 447--509 (1993; Zbl 0807.35030)] established for operators with real coefficients. A similar result holds for the Neumann problem.
scientific article; zbMATH DE number 5796747
scientific article