liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Sobolev spaces: with applications to elliptic partial differential equations
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2011 (English)Book (Refereed)
Abstract [en]

Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2011, 2. , 866 p.
, Grundlehren der mathematischen wissenschaften, ISSN 0072-7830 ; 342
Keyword [en]
46E35, 42B37, 26D10, Sobolev spaces, general domains, integral inequalities, isoperimetric and isocapacitary inequalities, spectrum of differential operators
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-72679ISBN: 978-3-642-15563-5ISBN: 3642155634OAI: diva2:461170

New, expanded and revised edition of Sobolev Spaces, originally published in the Springer Series in Soviet Mathematics (1985) Enhanced by many recent results Includes new applications to linear and nonlinear partial differential equations New historical comments, five new chapters and the significantly augmented list of references create a broader, modern view of the field.

Available from: 2011-12-02 Created: 2011-12-02 Last updated: 2013-03-20Bibliographically approved

Open Access in DiVA

No full text

Other links

Find book at a Swedish library/Hitta boken i ett svenskt bibliotekFind book in another country/Hitta boken i ett annat landGoogle Book Search

Search in DiVA

By author/editor
Maz'ya, Vladimir
By organisation
Applied MathematicsThe Institute of Technology
Natural Sciences

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 103 hits
ReferencesLink to record
Permanent link

Direct link