Skip to Main content Skip to Navigation
Journal articles

Analysis of a fractal boundary: the graph of the Knopp function

Abstract : A usual classification tool to study a fractal interface is the computation of its fractal dimension. But a recent method developed by Y. Heurteaux and S. Jaffard proposes to compute either weak and strong accessibility exponents or local Lp regularity exponents (the so-called p-exponent). These exponents describe locally the behavior of the interface. We apply this method to the graph of the Knopp function. The Knopp function itself has everywhere the same p-exponent. Nevertheless, using the characterization of the maxima and minima done by B. Dubuc and S. Dubuc, we will compute the p-exponent of the characteristic function of domain under the graph of F at each point (x,F(x)) and show that p-exponents, weak and strong accessibility exponents change from point to point. Furthermore we will derive a characterization of the local extrema of the function according to the values of these exponents.
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01037859
Contributor : Clothilde Melot <>
Submitted on : Wednesday, July 23, 2014 - 3:02:49 AM
Last modification on : Thursday, January 23, 2020 - 6:22:12 PM
Long-term archiving on: : Tuesday, November 25, 2014 - 11:46:19 AM

Files

preprint_SM_MB_CM.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01037859, version 1
  • ARXIV : 1407.6219

Collections

Citation

Mourad Ben Slimane, Clothilde Melot. Analysis of a fractal boundary: the graph of the Knopp function. Abstract and Applied Analysis, Hindawi Publishing Corporation, 2015, http://www.hindawi.com/journals/aaa/2015/587347/. ⟨hal-01037859⟩

Share

Metrics

Record views

267

Files downloads

196