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Journal Articles Journal of Fractal Geometry Year : 2023

h-Laplacians on Singular Sets

Claire David
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Until now, the correspondence between the Alexander-Kolmogorov Complex, and the De Rham one, by means of a small scale parameter, has not gone that far as passing to the limit of the resolvent of the associated Laplacian, when the small parameter tends towards zero. In this line, a result proving a complete Hodge decomposition was missing. We bridge this gap by means of our own rescaled h-cohomology, h being a very small parameter. Passing to the limit of the resolvent enables us to consider the extension to singular spaces, in particular, our h-differential operators also enable us to also make the connection with those of analysis on fractals, as introduced by Jun Kigami, and taken up by Robert S. Strichartz.
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Dates and versions

hal-03698953 , version 1 (19-06-2022)
hal-03698953 , version 2 (13-12-2022)



Claire David, Gilles Lebeau. h-Laplacians on Singular Sets. Journal of Fractal Geometry, In press, 10 (1), pp.61-108. ⟨10.4171/jfg/126⟩. ⟨hal-03698953v2⟩
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