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INTERPOLATION UNDER A GRADIENT BOUND

Published online by Cambridge University Press:  01 August 2009

GUNNAR ARONSSON
GUNNAR ARONSSON*
Affiliation:
Department of Mathematics, Linköping University, S-58183 Linköping, Sweden (email: guaro@mai.liu.se)
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Abstract

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This paper deals with the interpolation of given real boundary values into a bounded domain in Euclidean n-space, under a prescribed gradient bound. It is well known that there exist an upper solution (an inf-convolution) and a lower solution (a sup-convolution) to this problem, provided that a certain compatibility condition is satisfied. If the upper and lower solutions coincide somewhere in the domain, then several interesting consequences follow. They are considered here. Basically, the upper and lower solutions must be regular wherever they coincide.

Keywords

eikonalinfimal convolutionsupremal convolutioninterpolationuniqueness setweighted lengthshortest curveoptimal controlmaximum principlesemiconcave
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 1 , August 2009 , pp. 19 - 35
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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