New Developments in the Analysis of Nonlocal Operators

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 nonloc...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Danielli, Donatella
Otros Autores: Petrosyan, Arshak, Pop, Camelia A.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 2019.
Colección:Contemporary Mathematics Ser.
Temas:
Operator theory > Congresses.
Functional analysis > Congresses.
Differential equations > Congresses.
Théorie des opérateurs > Congrès.
Analyse fonctionnelle > Congrès.
Équations différentielles > Congrès.
Differential equations
Functional analysis
Operator theory
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Uniqueness for weak solutions of parabolic equations with a fractional time derivative1. Introduction; 2. Steklov averages; 3. Uniqueness; References; Boundary regularity for the free boundary in the one-phase problem; 1. Introduction; 1.1. Previous results and overview of the paper; 2. Preliminaries; 2.1. Existence; 2.2. Lipschitz regularity and flatness of; 2.3. Interior regularity of flat free boundaries; 3. Almost optimal regularity; 4. Optimal regularity; 4.1. Almgren's frequency formula; 4.2. Blowup; References
  • Fractional Laplacians on the sphere, the Minakshisundaram zeta function and semigroups1. Introduction; 2. Negative powers in the unit circle and the Hurwitz zeta function; 3. Positive powers in the unit circle and the Hurwitz zeta and Fine functions; 4. The semigroup generated by the Dirichlet-to-Neumann map; 5. Negative powers and the Minakshisundaram zeta function; 6. Positive powers and the Dirichlet-to-Neumann map; 7. Fractional Laplacians and the heat semigroup on the sphere. Extension problem and Harnack inequality; References; Obstacle problems for nonlocal operators; 1. Introduction
  • 1.1. Stationary obstacle problem1.2. Evolution obstacle problem; 1.3. Applications to mathematical finance; 1.3.1. Variance Gamma Process; 1.3.2. Regular Lévy Processes of Exponential type; 1.4. Comparison with previous research; 1.5. Structure of the paper; 2. Stationary obstacle problem; 3. Evolution obstacle problem; References; Back Cover

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