A Guide to Special Functions of Bounded Variation and Applications
Larsen, Christopher J.
2015, 250 p. 30 illus.
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An in depth look at special functions of bounded variation
The space Special Functions of Bounded Variation (SBV) has become critical for many applications, particularly in fracture mechanics and image processing, since its introduction in 1988. Inspite of this increased importance, the current literature on SBV provides a purely mathematical perspective and is written for an audience with a solid background in measure theory.
In this book the authors makes SBV more accessible to applied mathematicians and engineers. The material progresses systematically, beginning with an introduction and motivation and then providing a review of measure theory before moving on to more complex topics. Illustrations and examples are used to enhance the presentation.
This book will appeal to graduate students and researchers in the area of applied mathematics or engineering.
Preface.- Introduction and Motivation for SBV: Free Discontinuity Problems.- Review of Basic Measure Theory.- Relations Between Measures.- BV, Sets of Finite Perimeter, SBV, and Coarea.- Structure Related to Applications.- Applications.- Issues in Quasi-Static Evolution.- Bibliography.- Index