On the problem of the homotopy classification of elliptic boundary value problems. (Q1432505)

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.