Piecewise C1 Extremal Functions

  • John L. Troutman
Part of the Undergraduate Texts in Mathematics book series (UTM)


In many problems examined thus far we have required continuous differentiability of the function y (or Y) defining the classes for optimization. Already with the example of the minimal surface of revolution from §1.4(a) we have argued that for some configurations, the minimizing curve (if it exists) should exhibit “corners,” and it is natural to wonder whether cornered curves ŷ and Ŷ such as those shown in Figure 7.1 might not give improved results for other problems. Such curves are represented readily by functions which are piecewise continuously differentiable, or piecewise C1.


Minimal Surface Corner Point Local Extremal Extremal Function Comer Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • John L. Troutman
    • 1
  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA

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