New Developments in the Analysis of Nonlocal Operators
About this Title
Donatella Danielli, Purdue University, West Lafayette, IN, Arshak Petrosyan, Purdue University, West Lafayette, IN and Camelia A. Pop, University of Minnesota, Minneapolis, MN, Editors
Publication: Contemporary Mathematics
Publication Year: 2019; Volume 723
ISBNs: 978-1-4704-4110-4 (print); 978-1-4704-5151-6 (online)
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.
Graduate students and research mathematicians interested in analytic, geometric, and probabilistic aspects of nonlocal equations.
Table of Contents
- Nicola Garofalo – Fractional thoughts
- Mark Allen – Uniqueness for weak solutions of parabolic equations with a fractional time derivative
- Héctor Chang-Lara and Ovidiu Savin – Boundary regularity for the free boundary in the one-phase problem
- Pablo Luis De Nápoli and Pablo Raúl Stinga – Fractional Laplacians on the sphere, the Minakshisundaram zeta function and semigroups
- Donatella Danielli, Arshak Petrosyan and Camelia A. Pop – Obstacle problems for nonlocal operators