Lectures on Mappings of Finite Distortion [Paperback]

In this book we introduce the class of mappings of finite distortion as a generalization of the class of mappings of bounded distortion. Connections with models of nonlinear elasticity are also discussed. We study continuity properties, behavior of our mappings on null sets, topological properties like openness and discreteness, regularity of the potential inverse mappings and many other aspects.

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Introduction.- Continuity.- Openness and discreteness.- Images and preimages of null sets.- Homeomorphisms of finite distortion.- Integrability of Jf and 1/Jf.- Final comments.- Appendix.- References.

From the book reviews:

This book provides a detailed and organized study of mappings of finite distortion. It would be useful to anyone interested in this topic. Numerous open problems are posed and relevant references are provided throughout. (David Matthew Freeman, Mathematical Reviews, January, 2015)

In this book we introduce the class of mappings of finite distortion as a generalization of the class of mappings of bounded distortion. Connections with models of nonlinear elasticity are also discussed. We study continuity properties, behavior of our mappings on null sets, topological properties like openness and discreteness, regularity of the potential inverse mappings and many other aspects.

Self-contained introduction to an active, important and interesting field of research

Includes an Appendix with several basic results on Real Analysis, theory of Sobolev functions and Geometric Measure Theory

Suitable for any PhD student looking for an introduction to the subject

NL