The workshop «Secondary and delocalized index invariants» was held in Copenhagen, Denmark
11- 15 June 2018 the workshop «Secondary and delocalized index invariants» was held in Copenhagen, Denmark. The organizer of the event was University of Copenhagen (QS 79). Savin A. Yu., Doctor of Physics and Mathematics, professor of the Nilkolskii Mathematical Institute, gave a plenary talk: «On the index of elliptic problems in plane compound domains». The following problem was considered there. Let D be a compact plane domain with piecewise smooth boundary and we are also given a ﬁnite system of cuts of this domain by smooth curves. We consider diﬀerential equations in D with boundary conditions imposed along the boundary of D and transmission conditions along the cuts. Under appropriate ellipticity conditions, such problems have Fredholm property in weighted Sobolev spaces (with weights prescribed at the singular points on the boundary and inside the domain). In this talk, we address the index problem in this setting. The focus is on the contributions of the singular points to the index formula. It turns out that these contributions can be described as η-invariants of conormal symbols at the singular points and to deﬁne these η-invariants, we extend the deﬁnition of η-invariant due to Melrose to parameter-dependent boundary value problems.
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