Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (de Gruyter Nonlinear Analysis and Applications)

The scientific literature on the Hardy-Leray inequality, also known as the uncertainty principle, is very extensive and scattered. The Hardy-Leray potential shows an extreme spectral behavior and a peculiar influence on diffusion problems, both stationary and evolutionary. In this book, a big part of the scattered knowledge about these different behaviors is collected in a unified and comprehensive presentation. The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jürgen Appell, Würzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Jiguang Bao, Beijing, China Avner Friedman, Columbus, Ohio, USA Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Guozhen Lu, Storrs, CT, USA Wojciech Kryszewski, Toruń, Poland Vicenţiu D. Rădulescu, Kraków, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy–Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021) Preface Contents 1 Motivation of the Hardy–Leray potential 2 Looking at the Hardy–Leray potential 3 Calderón–Zygmund theory and the Hardy–Leray potential 4 Effect of the Hardy–Leray potential in the solvability of semilinear elliptic equations 5 The Hardy–Leray potential in semilinear heat equations 6 Elliptic equations with a nonlinearity on the gradient and the Hardy–Leray potential 7 The heat equation with nonlinearity on the gradient and the Hardy–Leray potential 8 Fractional Laplacian type operators 9 The fractional Hardy inequality 10 Calderón–Zygmund summability in the fractional setting 11 Fractional semilinear elliptic problems 12 The heat equation with fractional diffusion 13 The influence of the Hardy potential on the linear and semilinear fractional heat equations Bibliography Alphabetical Index