Square function estimates on layer potentials for higher-order elliptic equations

TL;DR

This paper proves square-function estimates for layer potentials associated with higher-order divergence-form elliptic operators with variable coefficients, extending known results from second-order and constant-coefficient cases to more general settings.

Contribution

It generalizes square-function estimates for layer potentials to arbitrary even-order variable-coefficient elliptic operators in the upper half-space.

Findings

Established square-function estimates for higher-order operators

Extended known results to variable coefficients and higher orders

Unified treatment for second-order and higher-order cases

Abstract

In this paper we establish square-function estimates on the double and single layer potentials for divergence-form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper half-space. This generalizes known results for variable-coefficient second-order operators, and also for constant-coefficient higher-order operators.