On the poisson equation with intersecting interfaces

Abstract

The interface problem is considered for the Poisson equation in two independent variables, The interface curves, along which jump conditions are prescribed, are allowed to intersect, The second derivatives of solutions of the interface problem are shown to lie in a certain "twisted" Soboiev space. The solution operator is shown to be a closed, densely defined, operator in L₂ whose domain can be determined exactly

^†This research was supported in part by National Science Foundation Grant NSF GP 9481 and in part by the Atomic Energy Commission under AEC AT(40-1)3443/3

^†This research was supported in part by National Science Foundation Grant NSF GP 9481 and in part by the Atomic Energy Commission under AEC AT(40-1)3443/3

Notes

^†This research was supported in part by National Science Foundation Grant NSF GP 9481 and in part by the Atomic Energy Commission under AEC AT(40-1)3443/3