© 2015

Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains


  • Comprehensive textbook on current theory of Sobolev spaces

  • Contains new results

  • One of the few books on the topic suitable for students


Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Mikhail S. Agranovich
    Pages 1-63
  3. Mikhail S. Agranovich
    Pages 65-110
  4. Mikhail S. Agranovich
    Pages 193-311
  5. Back Matter
    Pages 313-331

About this book


This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems.


The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory, and pseudodifferential operators, has included his own very recent findings in the present book.


The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems, and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date.


Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory, and mathematical physics will find this book particularly valuable.


Besov spaces Bessel potential spaces Lipschitz domain Sobolev-type spaces coercive problems elliptic boundary value problems

Authors and affiliations

  1. 1.MoscowRussia

Bibliographic information

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“This very interesting book presents a systematic study of elliptic problems in smooth and Lipschitz domains. … This modern graduate textbook is certainly an excellent starting point for any kind of further investigations. It is useful for specialists and researchers working in the fields of partial differential equations and mathematical physics. This book is also suitable as an introduction to the themes described above.” (Günter Berger, Mathematical Reviews, April, 2016)

“This book should be very useful for all mathematicians and mathematical physicists who want to learn the powerful techniques related to the properties of Sobolev spaces. It is also addressed to graduate students and young researchers interested in new ideas linking all the subjects involved.” (Vicenţiu D. Rădulescu, zbMATH 1322.46002, 2015)