Boundary value problems with global projection conditions |
| |
Authors: | B-W Schulze J Seiler |
| |
Institution: | a Institute of Mathematics, University of Potsdam, Postfach 601553, 14415 Potsdam, Germany b Institute of Mathematics, University of Hannover, Postfach 6009, 30060 Hannover, Germany |
| |
Abstract: | Parametrices of elliptic boundary value problems for differential operators belong to an algebra of pseudodifferential operators with the transmission property at the boundary. However, generically, smooth symbols on a manifold with boundary do not have this property, and several interesting applications require a corresponding more general calculus. We introduce here a new algebra of boundary value problems that contains Shapiro-Lopatinskij elliptic as well as global projection conditions; the latter ones are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. We show that every elliptic operator admits (up to a stabilisation) elliptic conditions of that kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. Moreover, we construct parametrices in the calculus. |
| |
Keywords: | Boundary value problems with APS-conditions Pseudodifferential operators on manifolds with boundary Ellipticity and parametrix constructions |
本文献已被 ScienceDirect 等数据库收录! |
|