Year: 2020
Type: preprint
Abstract: We solve the Neumann problem in the half space $\mathbb{R}^{n+1}_+$, for higher order elliptic differential equations with variable self-adjoint $t$-independent coefficients, and with boundary data in $L^p$, where $\max\bigl(1,\frac{2n}{n+2}-\varepsilon\bigr) < p < 2$. We also establish nontangential and area integral estimates on layer potentials with inputs in $L^p$ or $\dot W^{\pm1,p}$ for a similar range of~$p$, based on known bounds for $p\geq2$; in this case we may relax the requirement of self-adjointess.
Source: arXiv (Cornell University)
Author: Barton, Ariel
Institution: University of Arkansas at Fayetteville
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3004632196