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On some properties of the shortest curve in a compound domain

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Abstract

We consider a state space domain defined by a regular system of equality and inequality constraints. We study the properties of the shortest curve, that is, the curve that has the minimum length of all smooth curves joining two given points of the domain and lying entirely in the domain. If inequality constraints are absent, then the shortest curve is a geodesic. We show that the shortest curve is a function of the class W 2,∞, derive the equation of the shortest curve, and study some other properties of this curve.

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Authors and Affiliations

  1. Russian State Social University, Moscow, Russia

    A. V. Davydova & D. Yu. Karamzin

  2. Dorodnicyn Computing Center of the Russian Academy of Sciences, Moscow, Russia

    A. V. Davydova & D. Yu. Karamzin

Authors
  1. A. V. Davydova
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  2. D. Yu. Karamzin
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Correspondence to A. V. Davydova.

Additional information

Original Russian Text © A.V. Davydova, D.Yu. Karamzin, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 12, pp. 1647–1657.

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Davydova, A.V., Karamzin, D.Y. On some properties of the shortest curve in a compound domain. Diff Equat 51, 1626–1636 (2015). https://doi.org/10.1134/S0012266115120101

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