<span>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 dif
Recent Developments in Nonlocal Theory
โ Scribed by Giampiero Palatucci (editor); Tuomo Kuusi (editor)
- Publisher
- De Gruyter Open Poland
- Year
- 2018
- Tongue
- English
- Leaves
- 474
- Category
- Library
No coin nor oath required. For personal study only.
โฆ Synopsis
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.
โฆ Table of Contents
Contents
Preface
Essentials of Nonlocal Operators
Heat Kernels for Non-symmetric Non-local Operators
Fractional Harmonic Maps
Obstacle Problems Involving the Fractional Laplacian
Nonlocal Minimal Surfaces: Interior Regularity, Quantitative Estimates and Boundary Stickiness
Eigenvalue Bounds for the Fractional Laplacian: A Review
Recent Progress on the Fractional Laplacian in Conformal Geometry
Jump Processes and Nonlocal Operators
Regularity Issues Involving the Fractional p-Laplacian
Boundary Regularity, Pohozaev Identities and Nonexistence Results
Variational and Topological Methods for Nonlocal Fractional Periodic Equations
Change of Scales for Crystal Dislocation Dynamics
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