论文标题
纤维尖式操作员的Calderón投影仪
The Calderón Projector for Fibred Cusp Operators
论文作者
论文摘要
椭圆运算符$ p $的calderón投影仪与边界$ x $的多种多样是从一般边界数据到解决方案$ u $ o o $ pu = 0 $的一组边界数据的投影。 Seeley在1966年证明，对于紧凑型$ x $，对于$ p $均匀的椭圆形，到边界上有一个Calderón投影仪，它是$ \ partial x $的伪差操作员。我们将此结果概括为纤维尖晶型操作员的设置，这是一类椭圆运算符，这些椭圆运算符在某些非连接歧管上具有特殊的纤维结构。例如，这适用于某些局部对称空间或特定奇异空间上的拉普拉斯式，例如具有尖尖的域域或两个触摸平滑的严格凸出euclidean空间中的域的补体。我们的主要技术工具是Mazzeo和Melrose引入的$ ϕ $ -PseudoDifferentialCilculus。 在我们的演示文稿中，我们提供了一个可能对其他类型的奇点进行类似结构有用的设置。
A Calderón projector for an elliptic operator $P$ on a manifold with boundary $X$ is a projection from general boundary data to the set of boundary data of solutions $u$ of $Pu=0$. Seeley proved in 1966 that for compact $X$ and for $P$ uniformly elliptic up to the boundary there is a Calderón projector which is a pseudodifferential operator on $\partial X$. We generalize this result to the setting of fibred cusp operators, a class of elliptic operators on certain non-compact manifolds having a special fibred structure at infinity. This applies, for example, to the Laplacian on certain locally symmetric spaces or on particular singular spaces, such as a domain with cusp singularity or the complement of two touching smooth strictly convex domains in Euclidean space. Our main technical tool is the $ϕ$-pseudodifferential calculus introduced by Mazzeo and Melrose. In our presentation we provide a setting that may be useful for doing analogous constructions for other types of singularities.
