Gradients on Fractals

70 citations recorded by the source corpus.

How researchers see this paper

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Taylor Approximations on Sierpinski Gasket Type Fractals (2000, unknown): “After the completion of this paper, Teplyaev [ T2 ] proposed another approach to defining gradients.”
Energy measures and indices of Dirichlet forms, with applications to derivatives on some fractals (2009, background): “The concept that the total energy of f can be described as a square integral of a type of vector-valued gradient was first introduced by Kusuoka [10, 11] (see also [20] for a related work).”
Measurable Riemannian geometry on the Sierpinski gasket: the Kusuoka measure and the Gaussian heat kernel estimate (2008, background): “In [ 17 ], Teplyaev has studied gradient operator on post critically finite self-similar set and obtained some continuity results of gradient of certain functions.”
The Finite Element Method on the Sierpinski Gasket (2001, methodology): “Table 4.1. The exponents for the maximum (EMax), average (EAve), and energy (EEn) error, as estimated by comparison with the known solution for three different triharmonic functions (T1, T2 ,T3) and one quad-harmonic function (Q).”