Maria Rosaria Lancia - Böcker

This volume contains the proceedings of the AMS-SMF-EMS Special Session on Fractal Geometry in Pure and Applied Mathematics, held from July 5-9, 2022, in Grenoble, France. The volume includes papers on recent developments in fractal geometry and its applications, featuring both original research and expository summaries. Key topics include non-Brownian diffusion and randomized Dirichlet forms on Sierpinski gasket-type fractals, graph approximation of such fractals, heat diffusion across fractal boundaries and inverse problems on fractal domains. Some new results are also presented regarding Sobolev-type spaces on metric measure spaces, and function spaces related to iterated fractal drums like the Weierstrass curve.

Many problems coming from engineering, physics or biology are characterized by both the presence of di?erent temporal and spatial scales and the presence of contacts among di?erent components through (irregular) interfaces that often connect media with di?erent characteristics.