2010/01/28 by Tran Vu Khanh, Khanh, Tran Vu
Computer Science · Mathematics · #32D10 #32U05 #32V25 #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.CV #msc:32D10 #msc:32U05 #msc:32V25
paper · pdf · doi:10.48550/arxiv.1001.5093
A Thesis submitted for the degree of Doctor of Philosophy in front of the Committee composed by Joseph J. Kohn (President); Jeffery D. Mc.Neal; Emil J. Straube. Supervisor: Giuseppe Zampieri. 121 pages
arxiv created 2010/01/28 · openalex publication_date 2010/01/28 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This thesis deals with Partial Differential Equations in Several Complex Variables and especially focuses on a general estimate for the ∂-Neumann problem on a domain which is q-pseudoconvex or q-pseudoconcave at a boundary point z0. Generalizing Property (P) by \citeC84, we define Property (f\T-\M\T-P)k at z0. This property yields the estimate (f\T-\M)k \nof(Λ)\mathcal M u2≤ c(\no∂ u2+\no∂^*u2+\nou2)+C_\M\nou2-1 for any u∈ C^∞c(U∩ Ω)k∩ \TDom(\dib^*) where U is a neighborhood of z0. We want to point out that under a suitable choice of f and \M, (f\T-\M)k is the subelliptic, superlogarithmic, compactness and subelliptic multiplier estimate. The thesis also aims at exhibiting some relevant classes of domains which enjoy Property (f\T-\M\T-P)k and at discussing recent literature on the ∂-Neumann problem in the framework of this property.