A general method of weights in the d-bar-Neumann problem

الأصل · EN

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 C84, we define Property (f--P)ᵏ at z₀. This property yields the estimate (f-)ᵏ f(Λ)M u²≤ c(∂ u²+∂*u²+u²)+Cu²₋₁ for any u∈ C∞c(U∩ Ω)ᵏ∩ Dom() where U is a neighborhood of z₀. We want to point out that under a suitable choice of f and, (f-)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--P)ᵏ and at discussing recent literature on the ∂-Neumann problem in the framework of this property.