Fractional Sobolev Spaces And Inequalities PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Fractional Sobolev Spaces And Inequalities PDF full book. Access full book title Fractional Sobolev Spaces And Inequalities.
Author | : D. E. Edmunds |
Publisher | : Cambridge University Press |
Total Pages | : 170 |
Release | : 2022-10-13 |
Genre | : Mathematics |
ISBN | : 1009254642 |
Download Fractional Sobolev Spaces and Inequalities Book in PDF, ePub and Kindle
The fractional Sobolev spaces studied in the book were introduced in the 1950s by Aronszajn, Gagliardo and Slobodeckij in an attempt to fill the gaps between the classical Sobolev spaces. They provide a natural home for solutions of a vast, and rapidly growing, number of questions involving differential equations and non-local effects, ranging from financial modelling to ultra-relativistic quantum mechanics, emphasising the need to be familiar with their fundamental properties and associated techniques. Following an account of the most basic properties of the fractional spaces, two celebrated inequalities, those of Hardy and Rellich, are discussed, first in classical format (for which a survey of the very extensive known results is given), and then in fractional versions. This book will be an Ideal resource for researchers and graduate students working on differential operators and boundary value problems.
Author | : Giovanni Leoni |
Publisher | : American Mathematical Society |
Total Pages | : 605 |
Release | : 2023-03-17 |
Genre | : Mathematics |
ISBN | : 1470472538 |
Download A First Course in Fractional Sobolev Spaces Book in PDF, ePub and Kindle
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.
Author | : D. E. Edmunds |
Publisher | : Cambridge University Press |
Total Pages | : 169 |
Release | : 2022-10-31 |
Genre | : Mathematics |
ISBN | : 1009254634 |
Download Fractional Sobolev Spaces and Inequalities Book in PDF, ePub and Kindle
Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.
Author | : Giovanni Leoni |
Publisher | : American Mathematical Soc. |
Total Pages | : 626 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821847686 |
Download A First Course in Sobolev Spaces Book in PDF, ePub and Kindle
Sobolev spaces are a fundamental tool in the modern study of partial differential equations. In this book, Leoni takes a novel approach to the theory by looking at Sobolev spaces as the natural development of monotone, absolutely continuous, and BV functions of one variable. In this way, the majority of the text can be read without the prerequisite of a course in functional analysis. The first part of this text is devoted to studying functions of one variable. Several of the topics treated occur in courses on real analysis or measure theory. Here, the perspective emphasizes their applications to Sobolev functions, giving a very different flavor to the treatment. This elementary start to the book makes it suitable for advanced undergraduates or beginning graduate students. Moreover, the one-variable part of the book helps to develop a solid background that facilitates the reading and understanding of Sobolev functions of several variables. The second part of the book is more classical, although it also contains some recent results. Besides the standard results on Sobolev functions, this part of the book includes chapters on BV functions, symmetric rearrangement, and Besov spaces. The book contains over 200 exercises.
Author | : Ari Laptev |
Publisher | : Springer Science & Business Media |
Total Pages | : 414 |
Release | : 2009-12-02 |
Genre | : Mathematics |
ISBN | : 1441913416 |
Download Around the Research of Vladimir Maz'ya I Book in PDF, ePub and Kindle
The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theory, which is demonstrated, in particular, by presented new results and reviews from world-recognized specialists. Sobolev type spaces, extensions, capacities, Sobolev inequalities, pseudo-Poincare inequalities, optimal Hardy-Sobolev-Maz'ya inequalities, Maz'ya's isocapacitary inequalities in a measure-metric space setting and many other actual topics are discussed.
Author | : Joaquim Martín |
Publisher | : |
Total Pages | : 0 |
Release | : 2014 |
Genre | : Inequalities (Mathematics) |
ISBN | : 9782856297964 |
Download Fractional Sobolev Inequalities Book in PDF, ePub and Kindle
The authors obtain new oscillation inequalities in metric spaces in terms of the Peetre $K$-functional and the isoperimetric profile. Applications provided include a detailed study of fractional Sobolev inequalities and the Morrey-Sobolev embedding theorems in different contexts. In particular, the authors include a detailed study of Gaussian measures as well as probability measures between Gaussian and exponential. They show a kind of reverse Polya-Szego principle that allows them to obtain continuity as a self-improvement from boundedness, using symmetrization inequalities. The authors' methods also allow for precise estimates of growth envelopes of generalized Sobolev and Besov spaces on metric spaces. The authors also consider embeddings into BMO and their connection to Sobolev embeddings.
Author | : Kyril Tintarev |
Publisher | : Imperial College Press |
Total Pages | : 279 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 1860947972 |
Download Concentration Compactness Book in PDF, ePub and Kindle
Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volume fulfills the need for a source book that usefully combines a concise formulation of the method, a range of important applications to variational problems, and background material concerning manifolds, non-compact transformation groups and functional spaces. Highlighting the role in functional analysis of invariance and, in particular, of non-compact transformation groups, the book uses the same building blocks, such as partitions of domain and partitions of range, relative to transformation groups, in the proofs of energy inequalities and in the weak convergence lemmas.
Author | : Vladimir Maz'ya |
Publisher | : Springer |
Total Pages | : 506 |
Release | : 2013-12-21 |
Genre | : Mathematics |
ISBN | : 3662099225 |
Download Sobolev Spaces Book in PDF, ePub and Kindle
The Sobolev spaces, i. e. the classes of functions with derivatives in L , occupy p an outstanding place in analysis. During the last two decades a substantial contribution to the study of these spaces has been made; so now solutions to many important problems connected with them are known. In the present monograph we consider various aspects of Sobolev space theory. Attention is paid mainly to the so called imbedding theorems. Such theorems, originally established by S. L. Sobolev in the 1930s, proved to be a useful tool in functional analysis and in the theory of linear and nonlinear par tial differential equations. We list some questions considered in this book. 1. What are the requirements on the measure f1, for the inequality q
Author | : Luc Tartar |
Publisher | : Springer Science & Business Media |
Total Pages | : 219 |
Release | : 2007-05-26 |
Genre | : Mathematics |
ISBN | : 3540714839 |
Download An Introduction to Sobolev Spaces and Interpolation Spaces Book in PDF, ePub and Kindle
After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.
Author | : L. Saloff-Coste |
Publisher | : Cambridge University Press |
Total Pages | : 204 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780521006071 |
Download Aspects of Sobolev-Type Inequalities Book in PDF, ePub and Kindle
Focusing on Poincaré, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds, this text is an advanced graduate book that will also suit researchers.