Singular integral operators on non-compact manifolds and analysis on polyhedral domains
Victor Nistor
我们回顾了谎言流形(M,)的定义和假歧体运算符(M)的代数Ψ∞(M)的构造。 我们为 Ψ∞ (M) 中的伪差运算符(M) 提供了一些具体的 Fredholmness 条件,用于大型 Lie 歧化器 (M , ) 。 这些Fredholmness条件适用于多面体域的边界值问题和非紧凑流形上的非线性PDE。 作为应用程序,我们确定具有多圆柱端的歧体上的Dirac运算符的频谱。
We review the definition of a Lie manifold (M, ) and the construction of the algebra Ψ∞(M) of pseudodifferential operators on a Lie manifold (M, ). We give some concrete Fredholmness conditions for pseudodifferential operators in Ψ∞(M) for a large class of Lie manifolds (M, ). These Fredholmness conditions have applications to boundary value problems on polyhedral domains and to non-linear PDEs on non-compact manifolds. As an application, we determine the spectrum of the Dirac operator on a mani...