2020/02/06 by Ariel Barton, Barton, Ariel
Mathematics · #35C15 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Boundary (topology) #Boundary value problem #Combinatorics #Computer science #Economics #Elliptic curve #FOS: Mathematics #Mathematical analysis #Mathematical physics #Mathematics #Neumann boundary condition #Order (exchange) #Primary 35J30 #Pure mathematics #Range (aeronautics) #Secondary 31B10 #Space (punctuation) #Spectral Theory in Mathematical Physics #Variable (mathematics) #math.AP #msc:31B10 #msc:35C15 #msc:35J30
paper · pdf · doi:10.48550/arxiv.2002.02963
published in arXiv (Cornell University) (Cornell University) · 55 pages. arXiv admin note: text overlap with arXiv:1906.12234
arxiv created 2020/02/06 · openalex publication_date 2020/02/06 · arxiv updated 2020/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We solve the Neumann problem in the half space ℝn+1+, for higher order elliptic differential equations with variable self-adjoint t-independent coefficients, and with boundary data in Lp, where max(1,(2n)/(n+2)-ε) < p < 2. We also establish nontangential and area integral estimates on layer potentials with inputs in Lp or W±1,p for a similar range of~p, based on known bounds for p≥2; in this case we may relax the requirement of self-adjointess.