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Elliptic expansion-contraction problems on manifolds with boundary. (English. Russian original) Zbl 1354.58020
Dokl. Math. 94, No. 1, 393-395 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 469, No. 2, 154-156 (2016).
The interesting note under review deals with a class of expansion-contraction boundary value problems on manifolds with boundary. Precisely, problems of the type \[ (D,B): \quad H^s(M) \to H^{s-m}(M)\oplus H^{s-b}(X), \] \(m=\text{ord} D,\) \(b=\text{ord}B,\) are considered on a smooth compact manifold \(M\) with boundary \(X,\) where the main operator \(D\) and the boundary operator \(B\) are nonlocal and associated with smooth self-mappings of the manifold \(M.\)
The authors calculate the trajectory symbols of such problems and, by an analogue of the Shapiro–Lopatinskii condition, derive the corresponding finiteness theorem.
58J32 Boundary value problems on manifolds
47A53 (Semi-) Fredholm operators; index theories
35J30 Higher-order elliptic equations
Full Text: DOI
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