INTERPOLATION UNDER A GRADIENT BOUND
2009 (English)In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, ISSN 1446-7887, Vol. 87, no 1, 19-35 p.Article in journal (Refereed) Published
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 (ail 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.
Place, publisher, year, edition, pages
2009. Vol. 87, no 1, 19-35 p.
eikonal, infimal convolution, supremal convolution, interpolation, uniqueness set, weighted length, shortest curve, optimal control, maximum principle, semiconcave
IdentifiersURN: urn:nbn:se:liu:diva-51279DOI: 10.1017/S1446788709000044OAI: oai:DiVA.org:liu-51279DiVA: diva2:273926