Differential Equations on Fractals: A Tutorial

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Uniqueness of Brownian motion on Sierpinski carpets (2008, unknown): “See [2, 26, 43] for further information and references.”
A Hilbert Space Approach to Effective Resistance Metric (2009, background): “, [28,50].”
Fractal solids, product measures and fractional wave equations (2009, background): “…This journal is © 2009 The Royal Society2521 mathematicians began to look at partial differential equations—starting with Laplace’s or heat equation—on fractal (albeit non-random) sets (e.g. Kigami 2001; Strichartz 2006), an analogue of continuum physics and mechanics still needs to be developed.”
Developments in fractal geometry (2013, unknown): “Note that Strichartz [117] uses a less general deﬁnition of post-critically ﬁnite.”
Homogeneous trees of second order Sturm-Liouville equations: A general theory and program (2008, background): “One can find basic introduction to this analysis and references in [125, 206] and a survey of some exciting recent developments in [170] in [77].”
Geometrical Structure of Laplacian Eigenfunctions (2012, background): “A number of mathematical studies were devoted to the theory of partial differential equations on fractals in general and to localization of Laplacian eigenfunctions in particular (see [219, 374] and references therein).”
Heat Kernel Asymptotics for the Measurable Riemannian Structure on the Sierpinski Gasket (2012, background): “As studied in [1,23,34], a standard Dirichlet form .”