Abstract
This article introduces a constructive definition of contour integrals over fractal curves in the plane by making use the notion of oriented Iterated Function Systems and directional pseudo-measures. An expression for the contour integral of continuous functions over fractal interfaces is obtained through renormalization. As a result, a vector calculus on fractal interfaces which are boundaries of regular two-dimensional domains is developed by extending Green’s theorem in the plane also to fractal curves.
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© 1999 Springer-Verlag London Limited
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Giona, M. (1999). Vector Analysis on Fractal Curves. In: Dekking, M., Véhel, J.L., Lutton, E., Tricot, C. (eds) Fractals. Springer, London. https://doi.org/10.1007/978-1-4471-0873-3_11
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DOI: https://doi.org/10.1007/978-1-4471-0873-3_11
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1225-9
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