Publications

Research Papers

(Notes: Most are since 1994. The pdf files may be a little different from the published versions)

Fractals

with M. Barnsley and Orjan Stenflo, V-variable fractals: dimension results, Forum Mathematicum (to appear)

with M. Barnsley and Orjan Stenflo, V-variable fractals: fractals with partial self similarity, Advances in Math 218 (2008), no. 6, 2051--2088 (pdf 876 Kb).

with M. Barnsley and Örjan Stenflo, V-variable fractals and superfractals, a non-technical and somewhat informal overview (pdf 2.2Mb), updated 16 April 08.

with M. Barnsley and Orjan Stenflo, A fractal valued random itertion algorithm and fractal hieirarchy, Fractals 13 (2005), no. 2, 111--146. (pdf 1.8 Mb)

with Rüschendorf, Ludger. Random fractals and probability metrics. Adv. in Appl. Probab. 32 (2000), no. 4, 925--947. (pdf 230 Kb)

with Rüschendorf, Ludger. Selfsimilar fractals and selfsimilar random fractals. Fractal geometry and stochastics, II (Greifswald/Koserow, 1998), 109--123, Progr. Probab., 46, Birkhäuser, Basel, 2000. (pdf 168 Kb)

Deterministic and random fractals. Complex systems, 127--166, Cambridge Univ. Press, Cambridge, 2000. (pdf 340 Kb)

with Rüschendorf, Ludger. Random fractal measures via the contraction method. Indiana Univ. Math. J. 47 (1998), no. 2, 471--487. (pdf 188 Kb)

Fractals: a mathematical framework. Complex. Int. 2 (1995), 14 HTML documents (electronic). (pdf 244 Kb)
Also: Fractals and Self Similarity. Indiana Univ. Math. J. 30 (1981), no. 5, 713--747. (pdf 476 Kb)

For other related papers see Michael Barnsley's website.

Computational mathematics

with Dziuk, Gerhard. Finite Element Approximations to Surfaces of Prescribed Variable Mean Curvature, Num. Math. 102 (2006), no. 4, 611--648 (pdf 3.9 Mb)

with Dziuk, Gerhard. The discrete Plateau problem: algorithm and numerics. Math. Comp. 68 (1999), no. 225, 1--23. (pdf 1.7 Mb)

with Dziuk, Gerhard. The discrete Plateau problem: convergence results. Math. Comp. 68 (1999), no. 226, 519--546. (pdf 236 Kb)

with Dziuk, Gerhard. Finite element approximations and the Dirichlet problem for surfaces of prescribed mean curvature. Mathematical visualization (Berlin, 1997), 73--87, Springer, Berlin, 1998. (pdf 852 Kb)

with Dziuk, Gerhard. On the approximation of unstable parametric minimal surfaces, (title and abstract) Calc. Var. Partial Differential Equations 4 (1996), no. 1, 27--58. (pdf 252 Kb + 32 Kb)

with Dziuk, Gerhard. L² estimates for approximations to minimal surfaces. Curvature flows and related topics (Levico, 1994), 67--82, GAKUTO Internat. Ser. Math. Sci. Appl., 5, Gakkotosho, Tokyo, 1995. (pdf 156 Kb)

with Dziuk, Gerhard. A finite element method for the computation of parametric minimal surfaces. Equadiff 8 (Bratislava, 1993). Tatra Mt. Math. Publ. 4 (1994), 49--62. (pdf 160 Kb)

For related work see the following papers by Paola Pozzi (graduate student)

L² estimates for approximations to minimal surfaces. Math. Comp. 73 (2004), no. 248, 1763--1777

The discrete Douglas Problem : theory and numerics. Interfaces Free Bound. 6 (2004), no. 2, 219--252.

The discrete Douglas Problem: convergence results. IMA J. Numer. Anal. 25 (2005), no. 2, 337--378.

Geometric measure theory and analysis

with Ambrosio, Luigi; Fusco, Nicola. Higher integrability of the gradient and dimension of the singular set for minimisers of the Mumford-Shah functional. Calc. Var. Partial Differential Equations 16 (2003), no. 2, 187--215. (pdf 308 Kb)

with Tonegawa, Yoshihiro. Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory. Calc. Var. Partial Differential Equations 10 (2000), no. 1, 49--84. (pdf 268 Kb)

with Fang, Yi. Hessian energy and optimal parametrisations of surfaces. (title and abstract) Math. Z. 225 (1997), no. 3, 507--535. (pdf 208 Kb + 36 Kb)

with Fusco, Nicola. A direct proof for lower semicontinuity of polyconvex functionals. Manuscripta Math. 87 (1995)

with Fusco, Nicola. Partial regularity and everywhere continuity for a model problem from non-linear elasticity. J. Austral. Math. Soc. Ser. A 57 (1994), no. 2, 158--169.

Other papers are available at Research Reports

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Last updated: 16 April 2008