Recent Developments in Nonlocal Theory / / Giampiero Palatucci, Tuomo Kuusi.

• Author: Kuusi, Tuomo
• TeilnehmendeR: Kuusi, Tuomo,; Palatucci, Giampiero,
• Place / Publishing House: Warsaw ;, Berlin : : De Gruyter Open Poland, , [2018]; ©2017
• Year of Publication: 2018
• Language: English
• Physical Description: 1 online resource

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 contributorsClaudia 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.

Table of Contents

Frontmatter -- Contents -- Preface -- Essentials of Nonlocal Operators / Bucur, Claudia -- Heat Kernels for Non-symmetric Non-local Operators / Chen, Zhen-Qing / Zhang, Xicheng -- Fractional Harmonic Maps / Da Lio, Francesca -- Obstacle Problems Involving the Fractional Laplacian / Danielli, Donatella / Salsa, Sandro -- Nonlocal Minimal Surfaces: Interior Regularity, Quantitative Estimates and Boundary Stickiness / Dipierro, Serena / Valdinoci, Enrico -- Eigenvalue Bounds for the Fractional Laplacian: A Review / Frank, Rupert L. -- Recent Progress on the Fractional Laplacian in Conformal Geometry / González, María del Mar -- Jump Processes and Nonlocal Operators / Kassmann, Moritz -- Regularity Issues Involving the Fractional p-Laplacian / Kuusi, Tuomo / Mingione, Giuseppe / Sire, Yannick -- Boundary Regularity, Pohozaev Identities and Nonexistence Results / Ros-Oton, Xavier -- Variational and Topological Methods for Nonlocal Fractional Periodic Equations / Molica Bisci, Giovanni -- Change of Scales for Crystal Dislocation Dynamics / Patrizi, Stefania