Calderón projector

Summary

The Calderón projector of an elliptic differential operator $P$ on a domain $\Omega$ is a projection acting on boundary data. Its range is exactly the set of Cauchy data on $\partial\Omega$ of the solutions of $Pu = 0$ in $\Omega$. It is a matrix of pseudo-differential operators on the boundary. It reduces boundary value problems in $\Omega$ to equations on $\partial\Omega$, and it is the tool behind the general theory of elliptic boundary value problems.