A Gentle Invitation to the Fractional World / by Nicola Abatangelo, Serena Dipierro, Enrico Valdinoci.

Format:

Book

Author/Creator:

Abatangelo, Nicola.

Contributor:

Dipierro, Serena.

Valdinoci, Enrico.

Series:

La Matematica per il 3+2, 2038-5757 ; 176

Language:

English

Subjects (All):

Mathematical analysis.

Analysis.

Local Subjects:

Analysis.

Physical Description:

1 online resource (389 pages)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

The book focuses on the basic theory of nonlocal and fractional operators and it is divided into two main parts covering respectively the basic theory of the "singular-integral" fractional Laplacian operator, which also includes a number of explicit examples of its evaluations, and the regularity theory in L^p spaces, by going through Bessel and Besov spaces. A number of appendices then go over additional material in order to make the exposition as self-contained as possible. The book is suitable for a PhD course but can be also read by advanced undergraduates. It contains didactic elements, but it is also useful for researchers, since it collects essential material in a concise and self-constrained way.

Contents:

Chapter 1. Equivalent definitions of the fractional Laplacian

Chapter 2. Some explicit calculations of fractional Laplacians

Chapter 3. Liouville-type results

Chapter 4. Regularity theory in Lebesgue spaces for global solutions

Chapter 5. Interior regularity theory in Lebesgue spaces.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783032029522

OCLC:

1559220045