# On uniqueness results for Dirichlet problems of elliptic systems without DeGiorgi-Nash-Moser regularity

## TL;DR

This paper investigates the uniqueness of solutions to certain elliptic systems' Dirichlet problems without relying on classical regularity assumptions, introducing a new layer potential approach.

## Contribution

It develops a novel layer potential method to establish uniqueness for elliptic systems without regularity of solutions.

## Key findings

- Layer potentials are uniquely determined for these systems.
- A new representation for the fundamental solution substitutes classical methods.
- Uniqueness results hold under minimal regularity assumptions.

## 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.