Existence of the solution of classical smoothing problems with obstacles and weights
Abstract
We show that classical smoothing problems with obstacles and weights have always the solution. These problems are considered in quite general case, namely, we allow arbitrary dimension of variable and arbitrary degree in derivative part of functional to minimize. While the existence is proved without any assumption about the uniqueness of solution, some conditions assuring the uniqueness are also analyzed.
Keywords:
smoothing problems, natural spline, existence of solutionHow to Cite
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Copyright (c) 2012 The Author(s). Published by Vilnius Gediminas Technical University.
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Copyright (c) 2012 The Author(s). Published by Vilnius Gediminas Technical University.
License
This work is licensed under a Creative Commons Attribution 4.0 International License.