Elliptic boundary problems on manifolds with polycylindrical ends

Details Elliptic boundary problems on manifolds with polycylindrical ends Elliptic boundary problems on manifolds with polycylindrical ends

2005-08-25

arxiv.org/abs/math/0508516v1

Mathematics

Analysis of PDEs

33 pages

Scientific paper

We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we then deal with boundary value problems for cusp differential operators. We introduce an adapted Boutet de Monvel's calculus of pseudodifferential boundary value problems, and construct parametrices for elliptic cusp operators within this calculus. Fredholm solvability and elliptic regularity up to the boundary and up to infinity for boundary value problems on manifolds with polycylindrical ends follows.

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