Spelling suggestions: "subject:"imperators ono manifold with edge"" "subject:"imperators onn manifold with edge""
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Operators on corner manifolds with exit to infinityCalvo, D., Schulze, Bert-Wolfgang January 2005 (has links)
We study (pseudo-)differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y . The typical operators A are corner degenerate in a specific way. They are described (modulo ‘lower order terms’) by a principal symbolic
hierarchy σ(A) = (σ ψ(A), σ ^(A), σ ^(A)), where σ ψ is the interior symbol and
σ ^(A)(y, η), (y, η) 2 T*Y 0, the (operator-valued) edge symbol of ‘first generation’, cf. [15]. The novelty here is the edge symbol σ^ of ‘second generation’, parametrised by (z, Ϛ) 2 T*Z 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind.
We show the continuity of corner-degenerate operators in weighted edge Sobolev
spaces, and we investigate the ellipticity of edge symbols of second generation.
Starting from parameter-dependent elliptic families of edge operators of first
generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.
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Elliptic differential operators on manifolds with edgesSchulze, Bert-Wolfgang January 2006 (has links)
On a manifold with edge we construct a specific class of (edgedegenerate) elliptic differential operators. The ellipticity refers to the principal symbolic structure σ = (σψ, σ^) of the edge calculus consisting of the interior and edge symbol, denoted by σψ and σ^, respectively. For our choice of weights the ellipticity will not require additional edge conditions of trace or potential type, and the operators will induce isomorphisms between the respective edge spaces.
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