No abstract uploaded!

No abstract uploaded!

The modules of principal parts$P$^{$k$}($E$) of a locally free sheaf ε on a smooth scheme$X$is a sheaf of$O$_{$X$}-bimodules which is locally free as left and right$O$_{$X$}-module. We explicitly split the modules of principal parts$P$^{$k$}($O$($n$)) on the projective line in arbitrary characteristic, as left and right$O$_{p1}-modules. We get examples when the splitting-type as left module differs from the splitting-type as right module. We also give examples showing that the splitting-type of the principal parts changes with the characteristic of the base field.

We consider second order elliptic divergence form systems with complex measurable coefficients$A$that are independent of the transversal coordinate, and prove that the set of$A$for which the boundary value problem with$L$_{2}Dirichlet or Neumann data is well posed, is an open set. Furthermore we prove that these boundary value problems are well posed when$A$is either Hermitean, block or constant. Our methods apply to more general systems of partial differential equations and as an example we prove perturbation results for boundary value problems for differential forms.

No abstract uploaded!