Solvability of elliptic systems with square integrable boundary data

Abstract

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 PDEs and as an example we prove perturbation results for boundary value problems for differential forms.

This paper replaces its predecessor "A new approach to solvability of some elliptic pde's with square integrable boundary data" by the same authors