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On the problem of the homotopy classification of elliptic boundary value problems. (English. Russian original) Zbl 1066.58012
Dokl. Math. 63, No. 2, 174-178 (2001); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 377, No. 2, 165-169 (2001).
The authors first consider the classical boundary value problems, which is those satisfying the Atiyah-Bott condition. For these problems the homotopy classification is given. Afterwards, boundary value problems for elliptic equations that do not generally satisfy the Shapiro-Lopatinkii-Atiyah-Bott condition are dealt with. Under suitable assumptions a stable homotopy classification is given also for these cases.

58J32 Boundary value problems on manifolds
35S15 Boundary value problems for PDEs with pseudodifferential operators
58J20 Index theory and related fixed-point theorems on manifolds
58J40 Pseudodifferential and Fourier integral operators on manifolds