Quasiconformal Mappings and Sobolev Spaces

[52] Maz'ya, V. G. “On the extension of functions from the Sobolev spaces” (In Russian), Zapiski nauchnyh seminarov LOMI 1 (1981), 1–12. [53] Miklyukov, V. M. “On removable singularities of quasiconformal mappings in a space” (In ...

Quasiconformal Mappings and Sobolev Spaces

'Ht moi ..., si j'avait su comment en revenir, One lemce mathematics has rendered the je n'y serai. point aile.' human race. It has put common sense back Jule. Verne ... "'" it belong., on the topmost shelf next to the dusty caniller labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'~re of this series

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This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant
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This is the first volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume
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This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: