Articoli correlati a Functions of Bounded Variation and Free Discontinuity...
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This book deals with a class of mathematical problems which involve the minimization of the sum of a volume and a surface energy and have lately been refered to as 'free discontinuity problems'. The aim of this book is twofold: The first three chapters present all the basic prerequisites for the treatment of free discontinuity and other variational problems in a systematic, general, and self-contained way. In the later chapters, the reader is introduced to the theory of free discontinuity problems, to the space of special functions of bounded variation, and is presented with a detailed analysis of the Mumford-Shah image segmentation problem. Existence, regularity and qualitative properties of solutions are explained and a survey is given on the current knowledge of this challenging mathematical problem. Free discontinuity problems reveal a wide range of applications. The theory embodies classical problems, e.g. related to phase transitions, or fracture and plasticity in continuum mechanics, as well as more recent ones like edge detection in image analysis. This book provides the reader with a solid introduction to the field, written by principle contributors to the theory. The first half of the book contains a comprehensive and updated treatment of the theory of Functions of Bounded Variation and of the mathematical prerequisites of that theory, that is Abstract Measure Theory and Geometric Measure Theory.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Recensione
... an excellent account of the theory of BV functions. It should serve as a standard reference, especially for the BV theory, for years to come. (Bulletin of the London Mathematical Society)
Contenuti
- Measure Theory
- Basic Geometric Measure Theory
- Functions of bounded variation
- Special functions of bounded variation
- Semicontinuity in BV
- The Mumford-Shah functional
- Minimisers of free continuity problems
- Regularity of the free discontinuity set
- References
- Index
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
- EditoreOUP Oxford
- Data di pubblicazione2000
- ISBN 10 0198502451
- ISBN 13 9780198502456
- RilegaturaCopertina rigida
- LinguaInglese
- Numero di pagine452
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Functions of Bounded Variation and Free Discontinuity Problems (Oxford Mathematical Monographs)
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Oxford University Press, 2000
ISBN 10: 0198502451
ISBN 13: 9780198502456
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Functions of Bounded Variation and Free Discontinuity Problems (Hardcover)
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Hardcover. Condizione: new. Hardcover. This book deals with a class of mathematical problems which involve the minimization of the sum of a volume and a surface energy and have lately been refered to as 'free discontinuity problems'. The aim of this book is twofold: The first three chapters present all the basic prerequisites for the treatment of free discontinuity and other variational problems in a systematic, general, and self-contained way. In the later chapters, the reader is introduced to thetheory of free discontinuity problems, to the space of special functions of bounded variation, and is presented with a detailed analysis of the Mumford-Shah image segmentation problem. Existence, regularityand qualitative properties of solutions are explained and a survey is given on the current knowledge of this challenging mathematical problem. Free discontinuity problems reveal a wide range of applications. The theory embodies classical problems, e.g. related to phase transitions, or fracture and plasticity in continuum mechanics, as well as more recent ones like edge detection in image analysis. This book provides the reader with a solid introduction to the field, written by principlecontributors to the theory. The first half of the book contains a comprehensive and updated treatment of the theory of Functions of Bounded Variation and of the mathematical prerequisites of that theory,that is Abstract Measure Theory and Geometric Measure Theory. This book presents the reader with a systematic introduction to a class of variational problems called 'free discontinuity problems'. The book bridges the gap between the research level and elementary courses on measure theory and calculus of variation at a level suitable for graduate students. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9780198502456
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Functions of Bounded Variation and Free Discontinuity Problems (Hardcover)
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Oxford University Press, Oxford, 2000
ISBN 10: 0198502451
ISBN 13: 9780198502456
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Hardcover. Condizione: new. Hardcover. This book deals with a class of mathematical problems which involve the minimization of the sum of a volume and a surface energy and have lately been refered to as 'free discontinuity problems'. The aim of this book is twofold: The first three chapters present all the basic prerequisites for the treatment of free discontinuity and other variational problems in a systematic, general, and self-contained way. In the later chapters, the reader is introduced to thetheory of free discontinuity problems, to the space of special functions of bounded variation, and is presented with a detailed analysis of the Mumford-Shah image segmentation problem. Existence, regularityand qualitative properties of solutions are explained and a survey is given on the current knowledge of this challenging mathematical problem. Free discontinuity problems reveal a wide range of applications. The theory embodies classical problems, e.g. related to phase transitions, or fracture and plasticity in continuum mechanics, as well as more recent ones like edge detection in image analysis. This book provides the reader with a solid introduction to the field, written by principlecontributors to the theory. The first half of the book contains a comprehensive and updated treatment of the theory of Functions of Bounded Variation and of the mathematical prerequisites of that theory,that is Abstract Measure Theory and Geometric Measure Theory. This book presents the reader with a systematic introduction to a class of variational problems called 'free discontinuity problems'. The book bridges the gap between the research level and elementary courses on measure theory and calculus of variation at a level suitable for graduate students. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Codice articolo 9780198502456
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Functions of Bounded Variation and Free Discontinuity Problems (Hardcover)
Editore:
Oxford University Press, Oxford, 2000
ISBN 10: 0198502451
ISBN 13: 9780198502456
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Hardcover. Condizione: new. Hardcover. This book deals with a class of mathematical problems which involve the minimization of the sum of a volume and a surface energy and have lately been refered to as 'free discontinuity problems'. The aim of this book is twofold: The first three chapters present all the basic prerequisites for the treatment of free discontinuity and other variational problems in a systematic, general, and self-contained way. In the later chapters, the reader is introduced to thetheory of free discontinuity problems, to the space of special functions of bounded variation, and is presented with a detailed analysis of the Mumford-Shah image segmentation problem. Existence, regularityand qualitative properties of solutions are explained and a survey is given on the current knowledge of this challenging mathematical problem. Free discontinuity problems reveal a wide range of applications. The theory embodies classical problems, e.g. related to phase transitions, or fracture and plasticity in continuum mechanics, as well as more recent ones like edge detection in image analysis. This book provides the reader with a solid introduction to the field, written by principlecontributors to the theory. The first half of the book contains a comprehensive and updated treatment of the theory of Functions of Bounded Variation and of the mathematical prerequisites of that theory,that is Abstract Measure Theory and Geometric Measure Theory. This book presents the reader with a systematic introduction to a class of variational problems called 'free discontinuity problems'. The book bridges the gap between the research level and elementary courses on measure theory and calculus of variation at a level suitable for graduate students. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Codice articolo 9780198502456
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