Nontangential estimates on layer potentials and the Neumann problem for higher order elliptic equations

TL;DR

This paper establishes nontangential estimates for the Neumann problem and layer potentials associated with higher order divergence form elliptic operators with variable, t-independent coefficients, advancing boundary value problem theory.

Contribution

It introduces new nontangential estimates for the Neumann problem and layer potentials for higher order elliptic operators with variable coefficients, extending existing boundary value problem results.

Findings

Proves nontangential estimates for the Neumann problem.

Establishes nontangential estimates for higher order layer potentials.

Advances understanding of boundary behavior for higher order elliptic equations.

Abstract

We solve the Neumann problem, with nontangential estimates, for higher order divergence form elliptic operators with variable $t$-independent coefficients. Our results are accompanied by nontangential estimates on higher order layer potentials.