General second order, strongly elliptic systems in low dimensional nonsmooth manifolds. (Q2767866)

Let \(L\) be an arbitrary, strongly elliptic, formally self-adjoint, variable coefficient operator in two and three-dimensional Lipschitz domains; it is the goal of the paper to consider the Dirichlet Poisson problem in Sobolev-Besov scales. \(2\) introduces notation and definitions, gives some preliminary results and collects basic results. In \(3\) one can find a priori estimates on atomic Hardy spaces together with invertibility results for the single layer potential operator associated with \(L\). \(4\) and \(5\) contain many other properties of the single layer potential operator, in particular, the sharp invertibility region on Besov classes, applications to the Dirichlet Poisson problem on SobolevBesov spaces, the \(L^p\)-Dirichlet and regularity problems, fractional powers of \(L\), square root and Green function estimates, etc. The last \(6\) contains outline for further research, with a special emphasis on three-dimensional case.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00020].