On corner singularities of solutions to mixed boundary-value problems for second-order elliptic and parabolic equations
Jacek Banasiak, Gary F. Roach · Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences · 1991
Abstract In this paper we prove a decomposition formula for solutions of mixed boundary-value problems for elliptic and parabolic equations into regular and singular parts, which provides an explicit description of the behaviour of the solution near the corners of the boundary and also, in parabolic cases, shows how the singularity due to the corners varies in time. We also give some sufficient conditions for the regularity of the solution of time-dependent problems.