Title: On uniqueness results for Dirichlet problems of elliptic systems without DeGiorgi-Nash-Moser regularity,
Abstract: We study uniqueness of Dirichlet problems of second order divergence-form
elliptic systems with transversally independent coefficients on the upper
half-space in absence of regularity of solutions. To this end, we develop a
substitute for the fundamental solution used to invert elliptic operators on
the whole space by means of a representation via abstract single layer
potentials. We also show that such layer potentials are uniquely determined.