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A First Course in Fractional Sobolev Spaces
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A First Course in Fractional Sobolev Spaces
Series: Graduate Studies in Mathematics
Expected to ship within 12 - 17 working days
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This book provides a gentle introduction to fractional Sobolev
spaces which play a central role in the calculus of variations,
partial differential equations, and harmonic analysis. The first
part deals with fractional Sobolev spaces of one variable. It
covers the definition, standard properties, extensions, embeddings,
Hardy inequalities, and interpolation inequalities. The second part
deals with fractional Sobolev spaces of several variables. The
author studies completeness, density, homogeneous fractional
Sobolev spaces, embeddings, necessary and sufficient conditions for
extensions, Gagliardo-Nirenberg type interpolation inequalities,
and trace theory. The third part explores some applications:
interior regularity for the Poisson problem with the right-hand
side in a fractional Sobolev space and some basic properties of the
fractional Laplacian. The first part of the book is accessible to
advanced undergraduates with a strong background in integration
theory; the second part, to graduate students having familiarity
with measure and integration and some functional analysis. Basic
knowledge of Sobolev spaces would help, but is not necessary. The
book can also serve as a reference for mathematicians working in
the calculus of variations and partial differential equations as
well as for researchers in other disciplines with a solid
mathematics background. It contains several exercises and is
self-contained.
General
Imprint: |
American Mathematical Society
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Country of origin: |
United States |
Series: |
Graduate Studies in Mathematics |
Release date: |
2023 |
Authors: |
Giovanni Leoni
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Pages: |
579 |
ISBN-13: |
978-1-4704-7253-5 |
Categories: |
Books
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LSN: |
1-4704-7253-8 |
Barcode: |
9781470472535 |
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