On The Behavior Of The Sup And Inf Convolutions Of A Function Near The Boundary

Mathematics Research Report MRR95-050

On The Behavior Of The Sup And Inf Convolutions Of A Function Near The Boundary

Timothy R. Cranny

Abstract: 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.

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