On uniqueness results for Dirichlet problems of elliptic systems without DeGiorgi-Nash-Moser regularity
Pascal Auscher, Moritz Egert · HAL (Le Centre pour la Communication Scientifique Directe) · 2020
We study uniqueness of Dirichlet problems of second order divergence-form elliptic systems with transversally independent coefficients on the upper half-space in the 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.