The Neumann problem for higher order elliptic equations

Abstract

We solve the Neumann problem in the half space for higher order elliptic differential equations with variable self-adjoint t-independent coefficients, and with boundary data in the negative smoothness space where Our arguments are inspired by an argument of Shen and build on known well posedness results in the case p = 2. We use the same techniques to establish nontangential and square function estimates on layer potentials with inputs in Lp or for a similar range of p, based on known bounds for p near 2; in this case we may relax the requirement of self-adjointess.