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

Format:

Book

Author/Creator:

Kuusi, Tuomo

Contributor:

Kuusi, Tuomo, editor.

Palatucci, Giampiero, editor.

Language:

English

Physical Description:

1 online resource

Place of Publication:

Warsaw ; Berlin : De Gruyter Open Poland, [2018]

Language Note:

In English.

Summary:

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.

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

Notes:

This eBook is made available Open Access. Unless otherwise specified individually in the content, the work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) license: https://creativecommons.org/licenses/by-nc-nd/3.0 https://www.degruyter.com/dg/page/open-access-policy

Description based on online resource; title from PDF title page (publisher's Web site, viewed 15. Jun 2019)

ISBN:

9783110571561

3110571560

OCLC:

1032685254