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On the behaviour of the sup- and inf-convolutions of a function near the boundary
Published online by Cambridge University Press: 17 April 2009
Abstract
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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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- Copyright © Australian Mathematical Society 1996
References
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