2006 International Conference in Honor of Jacqueline Fleckinger.
Electronic Journal of Differential Equations,
Conference 16 (2007), pp. 185-192. 

Title: Permanence of metric fractals

Author: Kyril Tintarev (Uppsala Univ., Sweden)
 
Abstract: 
 The paper studies energy functionals on quasimetric spaces,
 defined by quadratic measure-valued Lagrangeans.
 This general model of medium, known as metric fractals,
 includes nested fractals and sub-Riemannian manifolds.
 In particular, the quadratic form of the Lagrangean satisfies
 Sobolev inequalities with the critical exponent determined
 by the (quasimetric) homogeneous dimension, which is also
 involved in the asymptotic distribution of the form's eigenvalues.
 This paper verifies that the axioms of the metric fractal are
 preserved by space products, leading thus to examples of
 non-differentiable media of arbitrary intrinsic dimension.

Published May 15, 2007.
Math Subject Classifications: 35J15, 35J20, 35J70, 43A85, 46E35.
Key Words: Fractals; Sobolev spaces; Dirichlet forms; homogeneous spaces.