Interface and mixed boundary value problems on n-dimensional polyhedral domains

摘要: Let � 2 Z+ be arbitrary. We prove a well-posedness result for mixed boundary value/interface problems of second-order, positive, strongly elliptic operators in weighted Sobolev spaces K �() on bounded, curvilinear polyhedral domain manifold M dimension n. The typical weightthat we consider is the (smoothed) distance to set singular points @. Our model problem Pu := −div(Ar u) = f, , u 0 @D, and D P @�, where function A >0 piece-wise smooth decomposition ¯ ( jj, @ @D @N into subsets corre- sponding, respectively, Dirichlet Neumann condi- tions. If there are no interfaces adjacent faces with Neu- mann conditions, our main gives an isomorphism : �+1