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