Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure - Pascal Auscher;Moritz Egert

In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents.  Prior to this work, only the two-dimensional situation was fully understood. In higher dimensions, partial results for existence in smaller ranges of exponents and for a subclass of such systems had been established.  The presented uniqueness results are completely new, and the authors also elucidate optimal ranges for problems with fractional regularity data.