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Full Description
This volume is based on the talks presented at the "New Frontiers in Homogenization and Fractional Calculus" conference, held at CRM-Barcelona on March 24-25, 2025. This event was organized to celebrate the 50th anniversary of the mathematical technique of Gamma-convergence, introduced by Ennio De Giorgi and Tullio Franzoni in 1975. Originally developed for applied purposes, this technique remains a fundamental tool in the study of various scientific phenomena, such as homogenization, phase transitions, and the asymptotic analysis of partial differential equations. At the same time, there has been a growing interest in the study of nonlocal problems, particularly due to their relevance in probability theory. In addition to representing a particularly challenging area of mathematics, these problems have become increasingly relevant in material science applications.
The contributions in this volume cover a wide range of topics and reflect the main areas of current research in variational convergence and nonlocal analysis. Additionally, as these techniques extend beyond pure analytical theory, the contributions explore numerical applications. This volume is aimed at students and researchers in mathematics, physics, and engineering who are interested in exploring recent developments in the theories of homogenization and fractional calculus.
Contents
Chapter 1. Singular-perturbation problems in fractional Sobolev spaces - recent results.- Chapter 2. A Survey on the Div-Curl Lemma and Some Extensions to Fractional Sobolev Spaces.- Chapter 3. The Polya-Szego principle in the fractional setting: a glimpse on nonlocal functional inequalities.- Chapter 4. Numerical Approximation of the logarithmic Laplacian via sinc-basis.- Chapter 5. A survey on the resolvent convergence.- Chapter 6. Fractional Sobolev spaces via interpolation, and applications to mixed local-nonlocal operators.- Chapter 7. Some results about strongly degenerate parabolic equations and forward-backward parabolic equations.- Chapter 8. A survey on anisotropic integral representation results.
