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.

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. (Viceniu D. Rdulescu, zbMATH 1322.46002, 2015)

Inhalt

Preface.- Preliminaries.- 1 The Spaces H s. .- 2 Elliptic Equations and Elliptic Boundary Value Problems.- 3 The Spaces H s and Second-Order Strongly Elliptic Systems in Lipschitz Domains.- 4 More General Spaces and Their Applications.- References.- Index.