Interface and mixed boundary value problems on \(n\)-dimensional polyhedral domains (Q612858)

The authors establish a well-posedness result for a general mixed boundary value problem on a curvilinear polyedral domain in a finite-dimensional manifold. The approach relies on the construction of suitable weighted Sobolev spaces. Interesting interface phenomena are analyzed through geometric techniques. Another main topic of the paper is the study of the regularity of the solution. The paper contains different other results, among them a weighted Hardy-Poincaré inequality is obtained.