Elementary properties of optimal irrigation patterns |
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Authors: | G Devillanova S Solimini |
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Institution: | (1) Laboratoire du CMLA, Ecole Normale Supérieure de Cachan, Cachan, France;(2) Dip. di Matematica, Politecnico di Bari, Bari, Italy |
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Abstract: | In this paper we follow the approach in Maddalena et al. (Interfaces and Free Boundaries 5, 391–415, 2003) to the study of the ramified structures and we identify some geometrical properties enjoyed by optimal irrigation
patterns. These properties are “elementary” in the sense that they are not concerned with the regularity at the ending points
of such structures, where the presumable selfsimilarity properties should take place. This preliminary study already finds
an application in G. Devillanova and S. Solimini (Math. J. Univ. Padua, to appear), where it is used in order to discuss the
irrigability of a given measure. |
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Keywords: | |
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