A first course in fractional Sobolev spaces
By: Leoni, Giovanni.
Series: Graduate studies in mathematics. ; no.229.Publisher: Providence American Mathematical Society 2023Description: xv, 586p.ISBN: 9781470472535.Subject(s): Function spaces | Sobolev spacesDDC classification: 515.782 | L554f Summary: 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.| Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
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PK Kelkar Library, IIT Kanpur | On Display | 515.782 L554f (Browse shelf) | Available | A186688 |
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| 515.353 L968n Navier–Stokes equations | 515.3530153205 T782l Lectures on Navier-Stokes equations | 515.3533 N28d Direct methods in the theory of elliptic equations | 515.782 L554f A first course in fractional Sobolev spaces | 515.782 L554f2 A first course in Sobolev spaces [2nd ed.] | 530.13 L629s Statistical mechanics and stochastic thermodynamics | 530.144 Sh93q Quantum many-body physics in a nutshell |
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.
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