{"paper":{"title":"The $\\dot W^{-1,p}$ Neumann problem for higher order elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ariel Barton","submitted_at":"2019-06-28T14:14:30Z","abstract_excerpt":"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 the negative smoothness space $\\dot W^{-1,p}$, where $\\max(0,\\frac{1}{2}-\\frac{1}{n}-\\varepsilon) <\\frac{1}{p} <\\frac{1}{2}$. Our arguments are inspired by an argument of Shen and build on known well posedness results in the case $p=2$.\n  We use the same techniques to establish nontangential and square function estimates on layer potentials with inputs in $L^p$ or $\\dot W^{\\pm1,p}$ for a similar "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.12234","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}