Fractals in Engineering: Theoretical Aspects and Numerical Approximations

Maria Rosaria Lancia is Professor of Mathematical Analysis at Sapienza University of Rome, where she received her PhD in  Applied and Theoretical Mechanics. Her current research interests are Fractal Analysis and Numerical approximation of BVPs in fractal domains. The emphasis is on linear, quasilinear and fractional BVPs in and within fractal domains possibly with dynamical boundary conditions and vector analysis on fractafolds. She is an editorial board member of Fractal and Fractional, MDPI and of the J. of Applied Mathematics and Computation, Hill Publishing Group.Anna Rozanova-Pierrat is Associate Professor of Applied Mathematics in CentraleSupélec, University Paris-Saclay, France. She obtained his PhD on Applied Mathematics in University Pierre et Marie Currie Paris 6 and RUDN (Moscow, Russia), where she finished her studies on Theoretical and Applied  Mathematics.  Her current research interests are motivated by physical and engineer problems (models of non linear acoustics, de Gennes hypothesis on the speed of the heat propagation between two media, shape optimization) involving irregular and fractal boundaries.

• C. Alberini and S. Finzi Vita, A numerical approach to a nonlinear diffusion model for self-organised criticality phenomena.- M. Cefalo et al., Approximation of 3D Stokes flows in fractal domains.- S. Fragapane, ∞-Laplacian obstacle problems in fractal domains.- M. Gabbard, Discretization of the Koch Snowflake Domain with Boundary and Interior Energies.- M.V. Marchi, On the dimension of the Sierpinski gasket in l2.- U. Mosco and M.A. Vivaldi, On the external approximation of Sobolev spaces by M-convergence.- A. Rozanova-Pierrat, Generalization of Rellich-Kondrachov theorem and trace compacteness for  fractal boundaries.