Symbolic calculus for boundary value problems on manifolds with edges |
| |
Authors: | D Kapanadze B-W Schulze |
| |
Institution: | 1.A. Razmadze Mathematical Institute,Academy of Sciences of Georgia,Tbilisi 93,Georgia;2.Institut für Mathematik,Universit?t Potsdam,Potsdam,Germany |
| |
Abstract: | Boundary value problems for (pseudo-) differential operators on a manifold with edges can be characterised by a hierarchy
of symbols. The symbolic structure is responsible for ellipticity and for the nature of parametrices within an algebra of
“edge-degenerate” pseudo-differential operators. The edge symbolic component of that hierarchy takes values in boundary value
problems on an infinite model cone, with edge variables and covariables as parameters. Edge symbols play a crucial role in
this theory, in particular, the contribution with holomorphic operator-valued Mellin symbols. We establish a calculus in a
framework of “twisted homogeneity” that refers to strongly continuous groups of isomorphisms on weighted cone Sobolev spaces.
We then derive an equivalent representation with a particularly transparent composition behaviour. |
| |
Keywords: | 35J40 35J70 35S15 58J40 |
本文献已被 SpringerLink 等数据库收录! |
|