The Method of Fischer-Riesz Equations for Elliptic Boundary Value Problems

Abstract EN

We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg.

To this end we reduce them to a boundary problem for a (possibly overdetermined) first-order system whose classical symbol has a left inverse.

For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula.

On using a well-elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem.