Author: Giovanni Molica BisciPublish On: 2016-03-11
This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators.
Author: Giovanni Molica Bisci
Publisher: Cambridge University Press
This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.
MR1011195 T. Komatsu, Uniform estimates for fundamental solutions associated with non-local Dirichlet forms, Osaka J. ... Servadei, Variational methods for nonlocal fractional problems, Encyclopedia of Mathematics and its Applications,
Author: Donatella Danielli
Publisher: American Mathematical Soc.
Category: Differential equations
This volume contains the proceedings of the AMS Special Session on New Developments in the Analysis of Nonlocal Operators, held from October 28–30, 2016, at the University of St. Thomas, Minneapolis, Minnesota. Over the last decade there has been a resurgence of interest in problems involving nonlocal operators, motivated by applications in many areas such as analysis, geometry, and stochastic processes. Problems represented in this volume include uniqueness for weak solutions to abstract parabolic equations with fractional time derivatives, the behavior of the one-phase Bernoulli-type free boundary near a fixed boundary and its relation to a Signorini-type problem, connections between fractional powers of the spherical Laplacian and zeta functions from the analytic number theory and differential geometry, and obstacle problems for a class of not stable-like nonlocal operators for asset price models widely used in mathematical finance. The volume also features a comprehensive introduction to various aspects of the fractional Laplacian, with many historical remarks and an extensive list of references, suitable for beginners and more seasoned researchers alike.
Bisci, G.M.; Radulescu, V.; Servadei, R. Variational methods for nonlocal fractional problems. With a foreword by Jean Mawhin. In Encyclopedia of Mathematics and its Applications, 162; Cambridge University Press: Cambridge,
Author: Francesco Mainardi
This book is a printed edition of the Special Issue "Fractional Calculus: Theory and Applications" that was published in Mathematics
 Jhaveri Y, Neumayer R: Higher Regularity of the Free Boundary in the
Obstacle Problem for the Fractional ... Servadei R: Variational Methods for Nonlocal Fractional Problems, Encyclopedia of Mathematics and its Applications,
Author: Giampiero Palatucci
Publisher: Walter de Gruyter GmbH & Co KG
This edited volume aims at giving an overview of recent advances in the theory and applications of Partial Differential Equations and energy functionals related to the fractional Laplacian operator as well as to more general integro-differential operators with singular kernel of fractional differentiability. After being investigated firstly in Potential Theory and Harmonic Analysis, fractional operators defined via singular integral are nowadays riveting great attention in different research fields related to Partial Differential Equations with nonlocal terms, since they naturally arise in many different contexts, as for instance, dislocations in crystals, nonlocal minimal surfaces, the obstacle problem, the fractional Yamabe problem, and many others. Much progress has been made during the last years, and this edited volume presents a valuable update to a wide community interested in these topics. List of contributors Claudia Bucur, Zhen-Qing Chen, Francesca Da Lio, Donatella Danielli, Serena Dipierro, Rupert L. Frank, Maria del Mar Gonzalez, Moritz Kassmann, Tuomo Kuusi, Giuseppe Mingione, Giovanni Molica Bisci, Stefania Patrizi, Xavier Ros-Oton, Sandro Salsa, Yannick Sire, Enrico Valdinoci, Xicheng Zhang.