OPERATORS ON CORNER MANIFOLDS WITH EXIT TO INFINITY

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Operators on manifolds with edge and conical exit to infinity Sobolev spaces with double weights on singular cones parameter-dependent ellipticity edge and corner symbols.
• 年，卷（期）: 2006,（2）
• 页码范围: 147-192
• 页数: 46页
• 分类号: O175.25|O175.3
• 语种: 英文

摘要

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 (σψ (A), σ∧ (A), σ∧ (A)), where σψ is the interior symbol and σ∧ (A)(y, η), (y, η) ∈ T*Y\0,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.