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A Collection of sharp dilation invariant integral inequalities for differentiable functions
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2008 (English)In: Sobolev Spaces in Mathematics I. Sobolev Type Inequalities / [ed] Vladimir Maz’ya, Berlin, Heidelberg: Springer , 2008, 223-248 p.Chapter in book (Other academic)
Abstract [en]

Presentation of new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics

  • The authors and editors are world-renowned specialists, working in different countries
  • Publication on the centenary of Sobolev’s birth with two short biographical articles and unique archive photos of S. Sobolev which have not yet been published in the English-language literature

This volume is dedicated to the centenary of the outstanding mathematician of the XXth century Sergey Sobolev and, in a sense, to his celebrated work On a theorem of functional analysis published in 1938, exactly 70 years ago, where the original Sobolev inequality was proved. This double event is a good case to gather experts for presenting the latest results on the study of Sobolev inequalities which play a fundamental role in analysis, the theory of partial differential equations, mathematical physics, and differential geometry. In particular, the following topics are discussed: Sobolev type inequalities on manifolds and metric measure spaces, traces, inequalities with weights, unfamiliar settings of Sobolev type inequalities, Sobolev mappings between manifolds and vector spaces, properties of maximal functions in Sobolev spaces, the sharpness of constants in inequalities, etc. The volume opens with a nice survey reminiscence My Love Affair with the Sobolev Inequality by David R. Adams.

Place, publisher, year, edition, pages
Berlin, Heidelberg: Springer , 2008. 223-248 p.
National Category
URN: urn:nbn:se:liu:diva-43171DOI: 10.1007/978-0-387-85652-0_6Local ID: 72259ISBN: 978-0-387-85648-3OAI: diva2:264030
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-06-17Bibliographically approved

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