Getting acquainted with the fractional Laplacian
Nicola Abatangelo, Enrico Valdinoci
TL;DR
This paper provides an introductory overview of the fractional Laplacian, aimed at undergraduates, covering basic concepts and recent research directions in elliptic PDEs involving this operator.
Contribution
It offers a beginner-friendly introduction to the fractional Laplacian, bridging classical and modern research without exhaustive detail.
Findings
Introduces the fractional Laplacian conceptually
Summarizes recent research trends in elliptic PDEs
Provides educational material for beginners
Abstract
These are the handouts of an undergraduate minicourse at the Universit\`a di Bari, in the context of the 2017 INdAM Intensive Period "Contemporary Research in elliptic PDEs and related topics". Without any intention to serve as a throughout epitome to the subject, we hope that these notes can be of some help for a very initial introduction to a fascinating field of classical and modern research.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Diverticular Disease and Complications