On some equations on non-smooth manifolds: canonical domains and model operators (Q1623356)

The main goal of the paper is to describe possible solvability conditions for the pseudo-differential equation on compact manifolds with boundary that contains conical points. More precisely the author is interested in invertibility of pseudo-differential near the conical point. The main theorem asserts that if the elliptic symbol admits wave factorization then the operator is invertible near the conical point and the corresponding a priori estimate holds. The uniqueness of the solution and the asymptotic representation for the solution are discussed. Moreover, the discrete variants are considered. For the entire collection see [Zbl 1392.46001].