an:06317114
Zbl 1298.58015
Savin, A. Yu.; Sternin, B. Yu.
Index of Sobolev problems on manifolds with many-dimensional singularities
EN
Differ. Equ. 50, No. 2, 232-245 (2014); translation from Differ. Uravn. 50, No. 2, 229-241 (2014).
0012-2661 1608-3083
2014
j
58J20 58J05 58J32
Sobolev (co)boundary problem; index problem; elliptic Sobolev problem; manifold with singularities
The theory of Sobolev problems is a theory of linear partial differential equations having boundary conditions on submanifolds of the initial smooth closed manifold. Later on, Sobolev problems were studied by the second author when the submanifold has singularities. The aim of that paper is to derive an index formula for the problem mentioned in the title. The authors reduce the Sobolev problem to a submanifold via pseudodifferential operators (\(\psi\)\,do) and translators which are not \(\psi\)\,do. Having in mind the theory of the translators including the corresponding index formulas see [the authors, ibid. 48, No. 12, 1577--1585 (2012); translation from Differ. Uravn. 48, No. 12, 1612--1620 (2012; Zbl 1267.35269) and ibid. 49, No. 4, 494--509 (2013); translation from Differ. Uravn. 49, No. 4, 513--527 (2013; Zbl 1274.58006)], they obtain in Theorem 2 explicit index formula for the elliptic Sobolev problem under investigation.
Petar Popivanov (Sofia)
1267.35269; 1274.58006