Randwertaufgaben halbzahliger charakteristik für eltiptische systeme

Abstract

This paper deals with boundary value problems of elliptic systems in the plane using W. Wendland's quite general quasinormal form. The usual periodicity condition for boundary data with respect to circulations around the boundary is weakened preserving local continuity of the boundary data and the Lopatinski condition which is satisfied everywhere on the boundary. This yields a half-integer for the characteristic (index) of the boundary condition instead of an integer in the classical case. Beyond that no other values of the characteristic are possible. Using a statement contained in R. Bott's periodicity theorem one can show that, assuming the general validity of the Lopatinski condition, two boundary conditions (with the same system dimension n) are continuously deformable into each other (i.e. homotopically equivalent) if and only if they have the same characteristic. W. Wendland's proof that the boundary value problem is semi-Fredholm remains valid for all boundary data which are periodic in the above...