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Lebesgue and Sobolev Spaces with Variable Exponents de Lars Diening

Lebesgue and Sobolev Spaces with Variable Exponents: Lecture Notes in Mathematics, cartea 2017

Autor Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Ruzicka
en Limba Engleză Paperback – 31 mar 2011
The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
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Specificații

ISBN-13: 9783642183621
ISBN-10: 364218362X
Pagini: 512
Ilustrații: IX, 509 p. 10 illus.
Dimensiuni: 155 x 235 x 30 mm
Greutate: 0.73 kg
Ediția:2011
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Graduate

Cuprins

1 Introduction.- 2 A framework for function spaces.- 3 Variable exponent Lebesgue spaces.- 4 The maximal operator.- 5 The generalized Muckenhoupt condition*.- 6 Classical operators.- 7 Transfer techniques.- 8 Introduction to Sobolev spaces.- 9. Density of regular functions.- 10. Capacities.- 11 Fine properties of Sobolev functions.- 12 Other spaces of differentiable functions.- 13 Dirichlet energy integral and Laplace equation.- 14 PDEs and fluid dynamics

Recenzii

From the reviews:
“The authors provide a comprehensive survey of the state of the art concerning Lebesgue and Sobolev spaces with variable exponents. … The book is also having a rich bibliography of 399 entries, a long list of symbols and an index. It will certainly become a standard reference in this field and stimulate further work in this direction.” (H. G. Feichtinger, Monatshefte für Mathematik, Vol. 165 (1), January, 2012)
“The book is devoted to Lebesgue and Soboley spaces with variable exponents. … The present book consists of the introduction and three parts. … The majority of the results presented in the monograph were obtained by the authors and their collaborators. … the books is a useful source of unified information on Lebesgue and Soboley spaces with variable exponents.” (Alexei Yu. Karlovich, Zentralblatt MATH, Vol. 1222, 2011)
“This book consists of three parts of different lengths and intentions, sub-divided into several chapters. There is a nice figure at the very beginning of the monograph explaining the dependencies among the chapters, together with some recommendations on which parts should be used for first reading or when teaching the subject in a graduate course. … the presentation can thus also be considered as a textbook and extremely useful reference for graduate students and researchers working in related fields … .” (Dorothee D. Haroske, Mathematical Reviews, January, 2013)

Textul de pe ultima copertă

The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Caracteristici

First book in the area of research Self-contained presentation suitable for both graduate students and researchers Comprehensive book with extensive index and nomenclature Applications for the developed theory is presented in the book Includes supplementary material: sn.pub/extras