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.

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References in corpus (3)

• The Green function estimates for strongly elliptic systems of second order
• The method of layer potentials in $L^p$ and endpoint spaces for elliptic operators with $L^{\infty }$ coefficients
• On the $L^p$-Poisson semigroup associated with elliptic systems