On the behaviour of the sup- and inf-convolutions of a function near the boundary
Timothy R. Cranny · Bulletin of the Australian Mathematical Society · 1996
The study of nonclassical solutions for elliptic and parabolic PDE's often involves the use of regularisation processes such as the sup- and inf-convolutions. In this note we study the behaviour of these regularised functions near the boundary of the domain, and derive constraints on the appropriate second-order sub- and superdifferentials on and near the boundary. Potential applications to regularity results are also noted.