Observations regarding compactness in the∂-Neumann problem
نویسندگان
چکیده
منابع مشابه
Compactness for the ∂ – Neumann problem – a Functional Analysis Approach
We discuss compactness of the ∂-Neumann operator in the setting of weighted Lspaces on Cn. For this purpose we use a description of relatively compact subsets of Lspaces. We also point out how to use this method to show that property (P) implies compactness for the ∂-Neumann operator on a smoothly bounded pseudoconvex domain and mention an abstract functional analysis characterization of compac...
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Compactness of the Neumann operator in the ∂̄-Neumann problem is studied for weakly pseudoconvex bounded Hartogs domains in two dimensions. A nonsmooth domain is constructed for which condition (P) fails to hold, yet the Kohn Laplacian still has compact resolvent. The main result, in contrast, is that for smoothly bounded Hartogs domains, the well-known sufficient condition (P) is equivalent to ...
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Here, and throughout the paper, we useD to denote the α-order derivative, where α is a multi-index and we are using standard multi-index notation. Moreover, γα := |α|!/α! denotes the polynomial coefficient. [The naturality of this choice of the Sobolev inner product will be pointed out and discussed below.] We define the Sobolev space W (Ω) to be the closure of C(Ω̄) with respect to the above in...
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ژورنال
عنوان ژورنال: Complex Variables and Elliptic Equations
سال: 2009
ISSN: 1747-6933,1747-6941
DOI: 10.1080/17476930902759478