# Bounds on layer potentials with rough inputs for higher order elliptic equations

## TL;DR

This paper derives square-function estimates for layer potentials associated with higher order elliptic equations with rough inputs, expanding understanding of boundary behavior for complex divergence form operators.

## Contribution

It establishes new square-function estimates for layer potentials of arbitrary even order elliptic operators with rough, t-independent coefficients in the upper half-space.

## Key findings

- Square-function estimates for layer potentials with rough inputs.
- Applicability to higher order divergence form elliptic operators.
- Enhanced understanding of boundary behavior for complex elliptic equations.

## Abstract

In this paper we establish square-function estimates on the double and single layer potentials with rough inputs for divergence form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper half-space.