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On the fractional Laplacian and nonlocal operators

Restrepo Montoya, Daniel Eduardo (2018) On the fractional Laplacian and nonlocal operators. Maestría thesis, Universidad Nacional de Colombia - Sede Medellín.

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The aim of this work is to study certain type of operators that have adquired a renewed relevance in the last decade. This wide class of operators, genericaly called nonlocal operators, appears naturally in many applications in physics, probability, biology and economics. Throughout this work our attention will be focused in a very important nonlocal operator known as the fractional Laplacian. This operator plays a similar role in the theory of nonlocal operators as the one played by the Laplacian in the classical theory of elliptic partial differential equations, i.e. the fractional Laplacian constitutes the most simple and, at the same time, the “model” nonlocal operator and therefore it is considered as the benchmark in the study of these kind of operators. Thus, by analogy, most of the relevant questions associated to the Laplacian (e.g. comparison principles, linear and nonlinear boundary value problems, and regularity results) have an equivalent for the fractional Laplacian. Also, in the same spirit of the multiplicity results for the classical semilinear partial differential equations we prove a multiplicity result for semilinear problems involving the fractional Laplacian using standard variational methods.

Tipo de documento:Tesis/trabajos de grado - Thesis (Maestría)
Colaborador / Asesor:Jiménez Urrea, José Manuel and Vélez López, Carlos Augusto
Información adicional:Maestría en Matemáticas
Palabras clave:Fractional Laplacian, Nonlocal operators, Variational methods
Temática:5 Ciencias naturales y matemáticas / Science > 51 Matemáticas / Mathematics
Unidad administrativa:Sede Medellín > Facultad de Ciencias > Escuela de Matemáticas
Código ID:64865
Enviado por : Daniel Eduardo Restrepo Montoya
Enviado el día :04 Julio 2018 20:53
Ultima modificación:27 Febrero 2019 19:29
Ultima modificación:27 Febrero 2019 19:29
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