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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

Timothy R. Cranny
Timothy R. Cranny
Affiliation:
Centre for Mathematics and Its ApplicationsAustralian National UniversityCanberra ACT 0200Australia
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 3 , June 1996 , pp. 515 - 520
Copyright
Copyright © Australian Mathematical Society 1996

References

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